Entropy Encoding and Decoding Scheme
Description
The present invention relates to entropy encoding and decoding and may be used in
applications such as, for example, video and audio compression.
Entropy coding, in general, can be considered as the most generic form of lossless data
compression. Lossless compression aims to represent discrete data with fewer bits than
needed for the original data representation but without any loss of information. Discrete
data can be given in the form of text, graphics, images, video, audio, speech, facsimile,
medical data, meteorological data, financial data, or any other form of digital data.
In entropy coding, the specific high-level characteristics of the underlying discrete data
source are often neglected. Consequently, any data source is considered to be given as a
sequence of source symbols that takes values in a given m-ary alphabet and that is
characterized by a corresponding (discrete) probability distribution [pl, ..., pm). In these
abstract settings, the lower bound of any entropy coding method in terms of expected
codeword length in bits per symbol is given by the entropy

Huffman codes and arithmetic codes are well-known examples of practical codes capable
of approximating the entropy limit (in a certain sense). For a fixed probability distribution,
Huffman codes are relatively easy to construct. The most attractive property of Huffman
codes is that its implementation can be efficiently realized by the use of variable-length
code (VLC) tables. However, when dealing with time-varying source statistics, i.e.,
changing symbol probabilities, the adaptation of the Huffman code and its corresponding
VLC tables is quite demanding, both in terms of algorithmic complexity as well as in terms
of implementation costs. Also, in the case of having a dominant alphabet value with
Pk> 0.5, the redundancy of the corresponding Huffman code (without using any alphabet
extension such as run length coding) may be quite substantial. Another shortcoming of
Huffman codes is given by the fact that in case of dealing with higher-order probability
modeling, multiple sets of VLC tables may be required. Arithmetic coding, on the other
hand, while being substantially more complex than VLC, offers the advantage of a more
consistent and adequate handling when coping with adaptive and higher-order probability

modeling as well as with the case of highly skewed probability distributions. Actually, this
characteristic basically results from the fact that arithmetic coding provides a mechanism,
at least conceptually, to map any given value of probability estimate in a more or less
direct way to a portion of the resulting codeword. Being provided with such an interface,
arithmetic coding allows for a clean separation between the tasks of probability modeling
and probability estimation, on the one hand, and the actual entropy coding, i.e., mapping of
a symbols to codewords, on the other hand.
An alternative to arithmetic coding and VLC coding is PIPE coding. To be more precise, in
PIPE coding, the unit interval is partitioned into a small set of disjoint probability intervals
for pipelining the coding processing along the probability estimates of random symbol
variables. According to this partitioning, an input sequence of discrete source symbols with
arbitrary alphabet sizes may be mapped to a sequence of alphabet symbols and each of the
alphabet symbols is assigned to one particular probability interval which is, in turn,
encoded by an especially dedicated entropy encoding process. With each of the intervals
being represented by a fixed probability, the probability interval partitioning entropy
(PIPE) coding process may be based on the design and application of simple variable-to-
variable length codes. The probability modeling can either be fixed or adaptive. However,
while PIPE coding is significantly less complex than arithmetic coding, it still has a higher
complexity than VLC coding.
Therefore, it would be favorable to have an entropy coding scheme at hand which enables
to achieve a better tradeoff between coding complexity on the one hand and compression
efficiency on the other hand, even when compared to PIPE coding which already combines
advantages of both arithmetic coding and VLC coding.
Further, in general, it would be favorable to have an entropy coding scheme at hand which
enables to achieve a better compression efficiency per se, at a moderate coding complexity.
Thus, it is an object of the present invention to provide an entropy coding concept which
fulfils the above-identified demand, i.e. enables to achieve a better tradeoff between coding
complexity on the one hand and compression efficiency on the other hand.
This object is achieved by an apparatus according to claim 1 or 23, a method according to
claim 49 or 50, and a computer program according to claim 51.
The present invention is based on the idea that decomposing a value range of the respective
syntax elements into a sequence of n partitions with coding the components of the syntax

element values z laying within the respective partitions separately with at least one by VLC
coding and with at least one by PIPE or arithmetic coding or any other entropy coding
method may greatly increase the compression efficiency at a moderate coding overhead in
that the coding scheme used may be better adapted to the syntax element statistics.
Accordingly, in accordance with embodiments of the present invention, syntax elements
are decomposed into a respective number n of source symbols s; with i=l...n, the
respective number n of source symbols depending on as to which of a sequence of n
partitions (140I-3) into which a value range of the respective syntax elements is sub-
divided, a value z of the respective syntax elements falls into, so that a sum of values of the
respective number of source symbols si yields z, and, if n>1, for all i=1...n-1, the value of
Si corresponds to a range of the ith partition
Further, some embodiments of the present invention, which use PIPE coding besides VLC
coding, exploit the fact that a better tradeoff between coding complexity on the one hand
and compression efficiency on the other hand may be achieved if in addition to the
categorizing feature of PIPE coding according to which alphabet symbols are distributed
among a plurality of specialized entropy en/decoders according to their probability
distribution estimate, a further categorizing stage is provided according to which source
symbols to be encoded are sub-divided into a first substream which is subject to VLC
coding, and a second substream which is - represented in the symbol alphabet of the PIPE
coder, i.e. as a sequence of alphabet symbols - subject to PIPE coding. By this measure,
source symbols having an appropriate symbol probability distribution, i.e. a probability
distribution suitable for being efficiently coded by means of VLC coding without the
deficiencies outlined above in the introductory portion of the specification of the present
application, may be categorized as VLC coded symbols such as the higher valued
partitions whereas other source symbols such as the lowest valued partitions may be
treated as PIPE coded symbols and subject to PIPE coding, the coding complexity of
which is higher than VLC coding, but at a better compression efficiency.
In accordance with an embodiment, it is possible to decompose syntax elements into a
respective integer number of source symbols, one of which being treated as VLC coded
symbol, the other one of which being treated as PIPE coded symbol.
Preferred aspects of the present invention are the subject of the enclosed dependent claims.
Preferred embodiments of the present invention are described below with respect to the
figures among which

Fig. 1a shows a block diagram of an entropy encoding apparatus according to an
embodiment;
Fig. lb shows a schematic diagram illustrating a possible decomposition of syntax
elements into source symbols according to an embodiment;
Fig. 1 c shows a flow diagram illustrating a possible mode of operation of decomposer of
Fig. la in decomposing syntax elements into source symbols according to an
embodiment;
Fig. 2a shows a block diagram of an entropy decoding apparatus according to an
embodiment;
Fig. 2b shows a flow diagram illustrating a possible mode of operation of composer of
Fig. 2a in composing syntax elements from source symbols according to an
embodiment;
Fig. 3 shows a block diagram of a PIPE encoder according to an embodiment which
may be used in Fig. 1;
Fig. 4 shows a block diagram of a PIPE decoder suitable for decoding a bitstream
generated by the PIPE encoder of Fig. 3, according to an embodiment, which
may be used in Fig. 2;
Fig. 5 shows a schematic diagram illustrating a data packet with multiplexed partial
bitstreams according to an embodiment;
Fig. 6 shows a schematic diagram illustrating a data packet with an alternative
segmentation using fixed-size segments according to a further embodiment;
Fig. 7 shows a block diagram of a PIPE encoder according to an embodiment using
partial bitstream interleaving;
Fig. 8 shows a schematic illustrating examples for the status of a codeword buffer at
the encoder side of Fig. 7 according to an embodiment;
Fig. 9 shows a block diagram of a PIPE decoder according to an embodiment using
partial bitstream interleaving;

Fig. 10 shows a block diagram of a PIPE decoder according to an embodiment using
codeword interleaving using a single set of codewords;
Fig. 11 shows a block diagram of a PIPE encoder according to an embodiment using
interleaving of fixed-length bit sequences;
Fig. 12 shows a schematic illustrating examples for the status of a global bit buffer at the
encoder side of Fig. 11 according to an embodiment;
Fig. 13 shows a block diagram of a PIPE decoder according to an embodiment using
interleaving of fixed-length bit sequences;
Fig. 14 shows a graph for illustrating an optimal probability interval discretization into
K = 4 intervals assuming a uniform probability distribution in (.0,0.5];
Fig. 15 shows a schematic diagram illustrating a tree of binary events for an LPB
probability of P =0.38 and an associated variable length code obtained by the
Huffman algorithm;
Fig. 16 shows a graph from which the relative bit rate increase ρ(P,C) for optimal
codes C given a maximum number of table entries Lm may be gathered;
Fig. 17 shows a graph illustrating the rate increase for the theorectically optimal
probability interval partitioning into K = 12 intervals and a real design with
V2V codes with a maximum number of Lm=65table entries;
Fig. 18 shows a schematic diagram illustrating an example for conversion of a ternary
choice tree into a full binary choice tree;
Fig. 19 shows a block diagram of a system comprising an encoder (left part) and
decoder (right part) according to an embodiment;
Fig. 20 shows a block diagram of an entropy encoding apparatus according to an
embodiment;

Fig. 21 shows a block diagram of an entropy decoding apparatus according to an
embodiment;
Fig. 22 shows a block diagram of an entropy encoding apparatus according to an even
further embodiment;
Fig. 23 shows schematic diagram illustrating examples for the status of a global bit
buffer at the encoder side of Fig. 22 according to an embodiment;
Fig. 24 shows a block diagram of an entropy decoding apparatus according to a further
embodiment of the present application.
Before several embodiments of the present application are described in the following with
respect to the figures, it is noted that equal reference signs are used throughout the figures
in order to denote equal or equivalent elements in these figures, and the description of
these elements presented with any of the previous figures shall also apply to any of the
following figures as far as the previous description does not conflict with the description of
the current figures.
Fig. 1 a shows an entropy encoding apparatus according to an embodiment of the present
application. The apparatus comprises a subdivider 100, a VLC encoder 102 and a PIPE
encoder 104.
The subdivider 100 is configured to subdivide a sequence of source symbols 106 into a
first subsequence 108 of source symbols and a second subsequence 110 of source symbols.
The VLC encoder 102 has an input thereof connected to a first output of subdivider 100
and is configured to symbol-wisely convert the source symbols of the first subsequence
108 into codewords forming a first bitstream 112. The VLC encoder 102 may comprise a
look-up table und use, individually, the source symbols as an index in order to look-up, per
source symbol, a respective codeword in the look-up table. The VLC encoder outputs the
latter codeword, and proceeds with the following source symbol in subsequence 110 in
order to output a sequence of codewords in which each codeword is associated with
exactly one of the source symbols within subsequence 110. The codewords may have
different lengths and may be defined such that no codeword forms a prefix with any of the
other codewords. Additionally, the look-up table may be static.
The PIPE encoder 104 has an input thereof connected to a second output of subdivider 100
and is configured to encode the second subsequence 110 of source symbols, represented in

form of a sequence of alphabet symbols, and comprises an assigner 114 configured to
assign a measure for an estimate of a probability distribution among possible values the
respective alphabet symbols may assume, to each alphabet symbol of the sequence of
alphabet symbols based on information contained within previous alphabet symbols of the
sequence of alphabet symbols, a plurality of entropy encoders 116 each of which is
configured to convert the alphabet symbols forwarded to the respective entropy encoder
into a respective second bitstream 118, and a selector 120 configured to forward each
alphabet symbol of the second subsequence 110 to a selected one of the plurality of
entropy encoders 116, the selection depending on the afore-mentioned measure for the
estimate of the probability distribution assigned to the respective alphabet symbol. The
association between source symbols and alphabet symbols may be such that each alphabet
symbol is uniquely associated with exactly one source symbol of subsequence 110 in order
to represent, along with possibly further alphabet symbols of the sequence of alphabet
symbols which may immediately follow each other, this one source symbol.
As described in more detail below, the sequence 106 of source symbols may be a sequence
of syntax elements of a parsable bitstream. The parsable bitstream may, for example,
represent video and/or audio content in a scalable or non-scalable manner with the syntax
elements representing, for example, transform coefficient levels, motion vectors, motion
picture reference indices, scale factors, audio envelope energy values or the like. The
syntax elements may, in particular, be of different type or category with syntax elements of
the same type, for example, having the same meaning within the parsable bitstream but
with respect to different portions thereof, such as different pictures, different macroblocks,
different spectral components or the like, whereas syntax elements of different type may
have a different meaning within the bitstream, such as a motion vector has a different
meaning than a syntax element representing a transform coefficient level representing the
motion prediction residual.
The subdivider 100 may be configured to perform the subdivision depending on the type of
the syntax elements. That is, subdivider 100 may forward syntax elements of a first group
of types to the first subsequence 108 and forward syntax elements of a second group of
types distinct from the first group, to the second subsequence 110. The subdivision
performed by subdivider 100 may be designed such that the symbol statistics of the syntax
elements within subsequence 108 is suitable for being VLC encoded by VLC encoder 102,
i.e. does result in almost a minimum entropy possible despite the use of VLC encoding and
its restriction with regard to its suitability for certain symbol statistics as outlined in the
introductory portion of the specification of the present application. On the other hand, the
subdivider 100 may forward all other syntax elements onto the second subsequence 110 so

that these syntax elements having symbols statistics not being suitable for VLC encoding,
are encoded by the more complex, but more efficient - in terms of compression ratio -
PIPE encoder 104.
As it is also the case with the more detailed described embodiments of the following
figures, the PIPE encoder 104 may comprise a symbolizer 122 configured to individually
map each syntax element of the second subsequence 110 into a respective partial sequence
of alphabet symbols, together forming the afore-mentioned sequence 124 of alphabet
symbols. In other words, the symbolizer 122 may not be present if, for example, the source
symbol of subsequence 110 are already represented as respective partial sequences of
alphabet symbols. The symbolizer 122 is, for example, advantageous in case the source
symbols within the subsequence 110 are of different alphabets, and especially, alphabets
having different numbers of possible alphabet symbols. Namely, in this case, the
symbolizer 122 is able to harmonize the alphabets of the symbols arriving within
substream 110. The symbolizer 122 may, for example, be embodied as a binarizer
configured to binarize the symbols arriving with in subsequence 110.
As mentioned before, the syntax elements may be of different type. This may also be true
for the syntax elements within substream 110. The symbolizer 122 may then be configured
to perform the individual mapping of the syntax elements of the subsequence 110 using a
symbolizing mapping scheme, such as a binarization scheme, different for syntax elements
of different type. Examples for specific binarization schemes are presented in the following
description, such as a unary binarization scheme, an exp-Golomb binarization scheme of
order 0 or order 1, for example, or a truncated unary binarization scheme, a truncated and
reordered exp-Golomb order 0 binarization scheme or a non-systematic binarization
scheme.
Accordingly, the entropy encoders 116 could be configured to operate on a binary
alphabet. Finally, it should be noted that symbolizer 122 may be regarded as being part of
the PIPE encoder 104 itself as shown in Fig. la. Alternatively, however, the binarizer may
be regarded as being external to the PIPE encoder,
Similar to the latter notice, it should be noted that the assigner 114, although shown to be
connected serially between symbolizer 122 and selector 120, may alternatively be regarded
as being connected between an output of symbolizer 124 and a first input of selector 120,
with an output of assigner 114 being connected to another input of selector 120 as later
described with respect to Fig. 3. In effect, the assigner 114 accompanies each alphabet
symbol with the afore-mentioned measure for an estimation of the probability distribution.

As far as the output of the entropy encoding apparatus of Fig. la is concerned, same is
composed of the first bitstream 112 output by VLC encoder 102 and the plurality of second
bitstreams 118 output by the plurality of entropy encoders 116. As further described below,
all these bitstreams may be transmitted in parallel. Alternatively, same may be interleaved
into a common bitstream 126 by use of an interleaver 128. The embodiments of Figs. 22 to
24 show examples with such bitstream interleaving. As further shown in Fig. 1, the PIPE
encoder 104 itself may comprise its own interleaver 130 in order to interleave the plurality
of second bitstreams 118 into a common PIPE coded bitstream 132. Possibilities for such
interleaver 130 are derivable from the following embodiments described with respect to
Figs. 5 to 13. Bitstream 132 and bitstream 112 may, in a parallel configuration, represent
the output of the entropy encoding apparatus of Fig. la. Alternatively, another interleaver
134 may interleave both bitstreams in which case interleaver 130 and 134 would form two
stages of one two-stage interleaver 128.
As has been described above, subdivider 100 may perform the subdivision syntax-element-
wise, i.e. the source symbols the subdivider 100 operates on may be whole syntax
elements, or alternatively speaking, subdivider 100 may operate in units of syntax
elements.
However, according to an alternative embodiment, the entropy encoding apparatus of Fig.
la may comprise decomposer 136 in order to decompose syntax elements within a parsable
bitstream 138 individually into one or more of the source symbols of the source symbol
sequence 106 entering subdivider 100. In particular, decomposer 136 may be configured to
convert the sequence 3 38 of syntax elements into the sequence 106 of source symbols by
individually decomposing each syntax element into a respective integer number of source
symbols. The integer number may vary among the syntax elements. In particular, some of
the syntax elements may even be left unchanged by decomposer 136, whereas other syntax
elements are decomposed in exactly two, or at least two, source symbols. The subdivider
100 may be configured to forward one of the source symbols of such decomposed syntax
elements to the first subsequence 108 of source symbols and another one of the source
symbols of the same decomposed syntax element to the second subsequence 110 of source
symbols. As mentioned above, the syntax elements within bitstream 138 may be of
different type, and the decomposer 136 may be configured to perform the individual
decomposing depending on the type of the syntax element. The decomposer 136 preferably
performs the individual decomposing of the syntax elements such that a predetermined
unique reverse mapping later on used at the decoding side, from the integer number of
source symbols to the respective syntax element, common for all syntax elements exists.

For example, the decomposer 136 may be configured to decompose syntax elements z in
parsable bitstream 138, into two source symbols x und y so that z = x + y, z = x- y, z = x • y
or z = x : y. By this measure, subdivider 100 may decompose the syntax elements into two
components, namely source symbols of source symbol stream 106, one of which is suitable
to be VLC encoded in terms of compression efficiency, such as x, and the other one of
which is not suitable for VLC encoding and is, therefore, passed on to the second
substream 110 rather than the first substream 108, such as y. The decomposition used by
decomposer 136 needs not to be bijective. However, as mentioned before, there should
exist a reverse mapping enabling a unique retrieval of the syntax elements of the possible
decompositions among which decomposer 136 may choose if the decomposition is not
bijective.
Up to now, different possibilities have been described for the handling of different syntax
elements. As to whether such syntax elements or cases exist, is optional. The embodiments
described herein below, however, concentrate on syntax elements which are decomposed
by decomposer 136 according to the following principle.
As show in Fig. lb, the decomposer 136 is configured to decompose certain syntax
elements z in parsable bitstream 138 in stages. Two or more stages may exist. The stages
are for dividing the value range of syntax element z into two or more adjacent subintervals
or sub-ranges as shown in Fig. lc. The value range of syntax element may have two
infinite endpoints, merely one or may have definite endpoints. In Fig. lc, the value range
of syntax element is exemplarily sub-divided into three partitions 140I-3. As shown in Fig.
lb, if the syntax element is greater or equal than the bound 142 of the first partition 140),
i.e. the upper limit separating partitions 1401 and 1402, then the syntax element is
subtracted by the bound limitl of the first partition 1401 and z is again checked as to
whether same is even greater or equal than the bound 144 of the second partition 1402, i.e.
the upper limit separating partitions 1402 and 1403, If z' is greater or equal than the bound
144, then z' is subtracted by the bound limit2 of the second partition 1402 resulting in z".
In the first case where z is smaller than limitl, the syntax element z is sent to subdivider
100 in plain. In case of z being between limitl and limit2, the syntax element z is sent to
subdivider 100 in as a tuple (limitl, z') with z=limitl+z', and in case of z being above
limit2, the syntax element z is sent to subdivider 100 in as a triplet (limitl, limit2-limitl,
z') with z=limitl+ limit2+z'. The first (or sole) component, i.e. z or limitl, forms a first
source symbol to be coded by subdivider 100, the second component, i.e. z' or limit2-
limitl, forms a second source symbol to be coded by subdivider 100, if present, and the
third component, i.e. z", forms a third source symbol to be coded by subdivider 100, if

present. Thus, in accordance with the embodiment of Fig. lb and lc, the syntax element is
mapped to any of 1 to 3 source symbols, but generalizations onto a less or more maximum
number of source symbols is readily derivable from the above description, and sue
alternatives will also be described in the folwing.
In any case, all these different components or resulting source symbols are according to the
below embodiments, coded with coding alternatives among. At least one of them is
forwarded by subdivider to PIPE coder 104, and at last another one thereof is sent to VLC
coder 102.
Particular advantageous embodiments are outlined in more detail below.
After having described above an embodiment for an entropy encoding apparatus, an
embodiment for an entropy decoding apparatus is described with respect to Fig. 2a. The
entropy decoding apparatus of Fig. 2a comprises a VLC decoder 200 and a PIPE decoder
202. The VLC decoder 200 is configured to code-wisely reconstruct source symbols of a
first subsequence 204 from codewords of a first bitstream 206. The first bitstream 206 is
equal to bitstream 112 of Fig. 1, and the same applies to subsequence 204 as far as
subsequence 108 of Fig. la is concerned. The PIPE decoder 202 is configured to
reconstruct a second subsequence 208 of source symbols, represented in the form of a
sequence of alphabet symbols, and comprises a plurality of entropy decoders 210, an
assigner 212 and a selector 214. The plurality of entropy decoders 210 are configured to
convert a respective one of second bitstreams 216 into alphabet symbols of the sequence of
alphabet symbols. The assigner 212 is configured to assign a measure of an estimate of a
probability distribution among the possible values the respective alphabet symbols may
assume, to each alphabet symbol of the sequence of alphabet symbols representing the
second subsequence 208 of source symbols to be reconstructed, based on information
contained within previously reconstructed alphabet symbols of the sequence of alphabet
symbols. To this end, assigner 212 maybe serially connected between an output of selector
214 and an input thereof, while further inputs of selector 214 have outputs of the entropy
decoders 210 respectively connected thereto. The selector 214 is configured to retrieve
each alphabet symbol of the sequence of alphabet symbols from a selected one of the
plurality of entropy decoders 210, the selection depending on the measure assigned to the
respective alphabet symbol. In other words, the selector 214 along with the assigner 212 is
operative to retrieve the alphabet symbols obtained by entropy decoders 210 in an order
among the entropy decoders 210 obtained by surveying information contained within
previous alphabet symbols of the sequence of alphabet symbols. In even other words,
assigner 212 and selector 214 are able to reconstruct the original order of the alphabet

symbols from alphabet symbol to alphabet symbol. Along with forecasting the next
alphabet symbol, assigner 212 is able to determine the afore-mentioned measure of the
estimate of the probability distribution for the respective alphabet symbol by use of which
selector 214 selects among the entropy decoders 210 to retrieve the actual value of this
alphabet symbol. To be even more precise, an as will be described in more detail below,
the PIPE decoder 202 may be configured to reconstruct the subsequence 208 of source
symbols, represented in form of the sequence of alphabet symbols, responsive to alphabet
symbol requests sequentially requesting for the alphabet symbols, and the an assigner 212
may be configured to assign to each request for an alphabet symbol of the sequence of
alphabet symbols representing the second subsequence (208) of source symbols to be
reconstructed, the afore-mentioned measure of an estimate of a probability distribution
among the possible values the respective alphabet symbol may assume. Accordingly, the
selector 214 may be configured to retrieve, for each request for an alphabet symbol of the
sequence of alphabet symbols representing the second subsequence (208) of source
symbols to be reconstructed, the respective alphabet symbol of the sequence of alphabet
symbols from a selected one of the plurality of entropy decoders 210, the selection
depending on the measure assigned to the respective request for the respective alphabet
symbol. The concordance between requests at the decoding side on the one hand, and the
data flow or encoding at the encoding side on the other hand will be outlined in more detail
with respect to Fig. 4.
As the first subsequence 214 of source symbols and the second subsequence 208 of source
symbols commonly form one common sequence 210 of source symbols, the entropy
decoding apparatus of Fig. 2a may, optionally, comprise a recombiner 220 configured to
recombine the first subsequence 204 and the second subsequence 208 to obtain the
common sequence 218 of source symbols. This common sequence 208 of source symbols
yields a reconstruction of sequence 106 of Fig. la.
In accordance with the description presented above with respect to Fig. 1, the source
symbols of the first and second subsequences 204 and 208 may be syntax elements of a
parsable bitstream. In this case, recombiner 220 could be configured to reconstruct this
parsable bitstream of the sequence 218 of syntax elements by interleaving the source
symbols arriving via first and second subsequences 204 and 208 in an order prescribed by
some parsing rule defining an order among the syntax elements. In particular, the syntax
elements may be, as described above, of different type and the recombiner 220 may be
configured to retrieve or request syntax elements of a first group of types from the VLC
decoder 200 via substream 204, and syntax elements of a second type from the PIPE
decoder 202 via substream 208. Accordingly, whenever the just-mentioned parsing rule

indicates that a syntax element of a type within the first group is the next in line,
recombiner 202 inserts an actual source symbol of subsequence 204 into common
sequence 218, and from subsequence 208 otherwise.
Likewise, the PIPE decoder 202 could comprise a desymbolizer 222 connected between
the output of selector 214 and an input of recombiner 220. Similar to the description above
with respect to Fig. 1, desymbolizer 222 could be regarded as being external to the PIPE
decoder 202 and could be even arranged behind recombiner 202, i.e. at the output side of
recombiner 220, alternatively. The desymbolizer 222 could be configured to remap, in
units of partial sequences of alphabet symbols, the sequence of alphabet symbols 224
output by selector 214 into the source symbols, i.e. syntax elements of subsequence 208.
Similar to recombiner 220, desymbolizer 222 knows about the construction of possible
partial sequences of alphabet symbols. In particular, desymbolizer 222 may analyze
recently received alphabet symbols from selector 214 in order to ascertain as to whether
these recently received alphabet symbols yield a valid partial sequence of alphabet symbols
associated with a respective value of the respective syntax element, or as to whether this is
not the case, and which alphabet symbol is missing next. In even other words, the
symbolizer 222 knows, at any time, as to whether further alphabet symbols have to be
received from selector 214 in order to finish the reception of a respective syntax element or
not, and accordingly, to which syntax element a respective one of the alphabet symbols
output by selector 214 belongs. To this end, the desymbolizer 222 may use a symbolizing
(de)mapping scheme differing for syntax elements of different type. Similarly, assigner
212 knows about the association of a current alphabet symbol to be retrieved from any of
the entropy decoders 210 by selector 214, to a respective one of the syntax elements and
may set the above-mentioned measure of estimation of a probability distribution of this
alphabet symbol accordingly, i.e. depending on the associated syntax element type. Even
further, assigner 212 may be differentiate between different alphabet symbols belonging to
the same partial sequence of a current alphabet symbol and may set the measure of
estimate of probability distribution differently for these alphabet symbols. Details in this
regard are described in more detail below. As describe therein, assigner 212 may be
configured to assign contexts to the alphabet symbols. The assignment may be dependent
on the syntax element type and/or the position within the partial sequence of alphabet
symbols of the current syntax element. As soon as assigner 212 has assigned a context to a
current alphabet symbol to be retrieved from any of the entropy decoders 210 by selector
214, alphabet symbol may inherently have the measure of estimate of probability
distribution associated therewith as each context has its measure of estimate associated
therewith. Further, the context - and its associated measure of estimate of probability
distribution - may be adapted according to the actual statistics of the alphabet symbols of

the respective context having been retrieved from the entropy decoders 210 so far. Details
in this regard are presented in more detail below.
Similar to the above discussion of Fig. 1, it may be possible that the correspondence
between the afore-mentioned source symbols of subsequences 204 and 208 in syntax
elements is not a one-to-one correspondence. Rather, the syntax elements may have been
decomposed into an integer number of sources symbols with the number, eventually,
varying among the syntax elements, but being, in any case, greater than one at least for one
syntax element. As noted above, the following embodiments focus on the handling of these
kind of syntax elements, and syntax elements of other kinds may even not be present.
For handling the just mentioned syntax elements, the entropy decoding apparatus of Fig. 2a
may comprise a composer 224 configured to redo the decomposition performed by
decomposer 136 of Fig. la. In particular, composer 224 may be configured to compose the
sequence 226 of syntax elements from the source symbols of sequence 218 or, if the
recombiner 220 is missing, subsequences 204 and 208, by individually composing each
syntax element from a respective integer number of source symbols with one of the source
symbols of the integer number of source symbols belonging to the first subsequence 204
and another one of the source symbols of the integer number of sources symbols of the
same syntax element belonging to the second subsequence 208. By this measure, certain
syntax elements may have been decomposed at the encoder side so as to separate
components suitable for VLC decoding from a remaining component having to be passed
through the PIPE decoding path. Similar to the above discussion, the syntax element may
be of different type and the composer 224 may be configured to perform the individual
composition depending on the type of the syntax elements. In particular, composer 224
may be configured to obtain the respective syntax elements by logically or mathematically
combining the integer number of source symbols of the respective syntax element. For
example, composer 224 may be configured, for each syntax element, apply +, -, : or • to
first and second source symbols of one syntax element.
As described above, the embodiments described herein below, however, concentrate on
syntax elements which are decomposed by decomposer 136 according to Fig. 1b and 1c
and the alternatives described regarding thereto. Fig. 2a shows as to how composer 224
may function to reconstruct these syntax elements from their source symbols 218.
As show in Fig. 2b, the composer 224 is configured to compose such syntax elements z in
stages from incoming source symbols s1 to sx with x being any of 1 to 3 in the present
example. Two or more stages may exist. As shown in Fig. 2b, composer 224 preliminaryly

sets z to be the first symbol s\ and checks as to whether z is equal to the first limitl. If this
is not case, z has been found. Otherwise, composer 224 adds the next source symbol S2 of
source symbol stream 218 to z and again checks as to whether this z equals limit2. If not, z
has been found. If not, composer 224 adds the next source symbol S3 of source symbol
stream 218 to z, in order to obtain z in its final form. Generalizations onto a less or more
maximum number of source symbols is readily derivable from the above description, and
such alternatives will also be described in the folwing.
In any case, all these different components or resulting source symbols are according to the
below embodiments, coded with coding alternatives among. At least one of them is
forwarded by subdivider to PIPE coder 104, and at last another one thereof is sent to VLC
coder 102.
Particular advantageous embodiments are outlined in more detail below. These Details
concentrate on favorable possibilities of dividing the value range of the syntax elements
and the entropy VLC and PIPE coding schemes which may be used to encode the source
symbols.
Further, as has also been described above with respect to Fig. 1, the entropy decoding
apparatus of Fig. 2a may be configured to receive the first bitstream 206 as well as the
plurality of second bitstreams 216 separately or in an interleaved form by way of an
interleaved bitstream 228. In the latter case, entropy decoding apparatus of Fig. 2a may
comprise a deinterleaver 230 configured to deinterleave the interleaved bitstream 228 to
obtain the first bitstream 206 on the one hand and the plurality of second bitstreams 216 on
the other hand. Similar to the above discussion of Fig. 1, the deinterleaver 230 may be
subdivided into two stages, namely a deinterleaver 232 for deinterleaving the interleaved
bitstream 228 into two parts, namely bitstream 206 on the one hand and an interleaved
form 234 of the second bitstream 216 on the other hand, and a deinterleaver 236 for
deinterleaving the latter bitstream 234 to obtain the individual bitstreams 216.
Thus, Fig. la and Fig. 2a showed an entropy encoding apparatus on the one hand and an
entropy decoding apparatus suitable for decoding the encoding result obtained by the
entropy encoding apparatus of Fig. 1, on the other hand. Details regarding many of the
elements shown in Fig. la and 2 are described in more detail with regard to the further
figures. Accordingly, reference is made to these details in the following description and
these details shall be regarded as also applying to the embodiments of Fig. la and 2
individually, as far as these details are separately implementable in the above-described
embodiments. Merely with respect to the interleavers and deinterleavers 132 and 234,

some additional notice is made here. In particular, interleaving of the bitstreams 112 and
118 may be favorable in case the bitstreams have to be multiplexed into one channel in
order to be transmitted. In this case, it may be favorable to interleave the VLC bitstream
112 on the one hand and the PIPE encoding bitstreams 118 on the other hand so as to obey
certain conditions to be met such as obeying some maximum decoding delay. In even other
words, it may be necessary that the relative time displacement between the times the
syntax elements and source symbols, respectively, are retrievable at the decoding side on
the one hand and the relative displacement in time in accordance with their position in the
parsable bitstream on the other hand, does not exceed a certain maximum delay. Many
alternatives for solving this problem are described below. One of these possibilities
involves the entropy encoders 116 to be of a variable length coder type configured to map
alphabet symbol sequences to codewords, and the entropy decoders 210 to do the reverse
mapping. The codewords of VLC bitstream 112 and PIPE bitstreams 118 may be, but do
not have to be, selected such that no codeword of any of these bitstreams is prefix of any
codeword of any of the other bitstreams, so that the codeword borders remain uniquely
determinable at the decoder side. In any case, the interleaver 128 may be configured to
reserve and buffer a sequence of codeword entries for the codeword within the first
bitstream 112 and the second bitstream 118 in a sequential order depending on an order in
which the alphabet symbols of the sequence 124 of alphabet symbols forwarded by the
selector 120 to the plurality of entropy encoders 116 result in a beginning of a new
alphabet symbol sequence to be mapped to a respective codeword at the respective entropy
encoder 116 and a new source symbol of the second substream 108 is mapped by the VLC
encoder 102, respectively. In other words, interleaver 128 inserts the codewords of
bitstream 112 into the common bitstream 126 in the order of the source symbols from
which they have been obtained by VLC encoding, in their order within substream 108 and
source symbol stream 106, respectively. Codewords output by entropy encoders 116 are
inserted into the common bitstream 126 between consecutive ones of the codewords of the
VLC bitstream 112. Owing to the PIPE encoding categorization of the alphabet symbols by
assigner 114 and selector 120, respectively, each of the codewords of the entropy encoders
116 have alphabet symbols of different source symbols of substream 110 encoded therein.
The position of the codewords of the PIPE encoded bitstreams 118 within the common
bitstream 126 among each other and relative to the VLC codeword of bitstream 112 is
determined by the first alphabet symbol encoded in each codeword, respectively, i.e. the
oldest one in time. The order of these primary alphabet symbols encoded into the
codewords of bitstreams 118 in the alphabet symbol stream 124 determines the order of the
codewords of bitstreams 118 within the common bitstream 126 among each other; relative
to the VLC codewords of bitstream 112, the source symbol to which these primary
alphabet symbols encoded into the codewords of bitstreams 118 belong, determine

between which consecutive codewords of bitstream 112 the respective codeword of any of
bitstreams 118 is to be positioned. In particular, the consecutive VLC codewords between
which the respective codeword of any of bitstreams 118 is to be positioned, are those
between which the source symbol of substream 110 is positioned in accordance with the
original order of un-subdivided source symbol stream 106, to which the respective primary
alphabet symbol encoded into the respective codeword of bitstreams 118 belongs. The
interleaver 128 may be configured to remove codewords entered into the afore-mentioned
codeword entries in sequential order to obtain the common bitstream 126 of interleaved
codewords. As has already been described above, the entropy encoders 116 may be
configured to sequentially enter their codewords into the codeword entries reserved for the
respective entropy encoder 116 and the selector 120 may be configured to forward the
alphabet symbols representing the source symbols of the second substream 110 in an order
maintaining an order in which the source symbols of the first substream 108 and the
second substream 110 were interleaved within the sequence 106 of source symbols.
Additional measures may be provided in order to cope with situations where certain ones
of the entropy encoders 116 are selected such seldom that it takes to long a time to obtain a
valid codeword within that very rarely used entropy encoder 116. Examples for such
measures are described in more detail below. In particular, the interleaver 128 along with
the entropy encoder 116 may, in this case, be configured to flush their alphabet symbols
collected so far and codewords having been entered into the afore-mentioned codeword
entries, respectively, in a manner so that the time of this flushing procedure may be
forecasted or emulated at the decoding side,
At the decoding side, the deinterleaver 230 may act in the reverse sense: whenever, in
accordance with the afore-mentioned parsing scheme, the next source symbol to be
decoded, is a VLC coded symbol, a current codeword within common bitstream 228 is
regarded as a VLC codeword and forwarded within bitstream 206 to VLC decoder 200. On
the other hand, whenever any of the alphabet symbols belonging to any of the PIPE
encoded symbols of substream 208 is a primary alphabet symbol, i.e. necessitates a new
mapping of a codeword of a respective one of the bitstreams 216 to a respective alphabet
symbol sequence by the respective entropy decoder 210, the current codeword of common
bitstream 228 is regarded as a PIPE encoded codeword and forwarded to the respective
entropy decoder 210. The detection of the next codeword border, i.e. the detection of the
extension of the next codeword from the end of the codeword just having been forwarded
to any of the decoders 200 and 202, respectively, to its end within the inbound interleaved
bitstream 228 may be deferred, and be performed under knowledge of, the decoder 200 and
202 being the dedicated recipient of this next codeword in accordance with the above-

outlined rule: based on this knowledge, the codebook used by the recipient decoder is
known and the respective codeword detectable. If, on the other hand, the codebooks would
be designed such that the codeword borders would be detectable without the a-priori
knowledge about the recipient decoder among 200 and 202, then the codeword separation
could be performed in parallel. In any case, due to the interleaving, the source symbols are
available at the decoder in an entropy decoded form, i.e. as source symbols, in their correct
order at reasonable delay.
After having described above embodiments for an entropy encoding apparatus and a
respective entropy decoding apparatus, next more detailed embodiments for the above-
mentioned PIPE encoders and PIPE decoders are described.
A PIPE encoder according to an embodiment is illustrated in Fig. 3. Same may be used as
PIPE encoder in Fig. la. The PIPE encoder losslessly converts a stream of source
symbols 1 into a set of two or more partial bitstreams 12. Each source symbol 1 my be
associated with a category or type of a set of one or more categories or types. As an
example, the categories can specify the type of the source symbol. In the context of hybrid
video coding, a separate category may be associated with macroblock coding modes, block
coding modes, reference picture indices, motion vector differences, subdivision flags,
coded block flags, quantization parameters, transform coefficient levels, etc. In other
application areas such as audio, speech, text, document, or general data coding, different
categorizations of source symbols are possible.
In general, each source symbol can take a value of a finite or countable infinite set of
values, where the set of possible source symbol values can differ for different source
symbol categories. For reducing the complexity of the encoding and decoding algorithm
and for allowing a general encoding and decoding design for different source symbols and
source symbol categories, the source symbols 1 are converted into ordered sets of binary
decisions and these binary decisions are then processed by simple binary coding
algorithms. Therefore, the binarizer 2 bijectively maps the value of each source symbol 1
onto a sequence (or string) of bins 3. The sequence of bins 3 represents a set of ordered
binary decisions. Each bin 3 or binary decision can take one value of a set of two values,
e.g. one of the values 0 and 1. The binarization scheme can be different for different source
symbol categories. The binarization scheme for a particular source symbol category can
depend on the set of possible source symbol values and/or other properties of the source
symbols for the particular category. Table 1 illustrates three example binarization schemes
for countable infinite sets. Binarization schemes for countable infinite sets can also be
applied for finite sets of symbol values. In particular for large finite sets of symbols values,

the inefficiency (resulting from unused sequences of bins) can be negligible, but the
universality of such binarization schemes provides an advantage in terms of complexity
and memory requirements. For small finite sets of symbol values, it is often preferable (in
terms of coding efficiency) to adapt the binarization scheme to the number of possible
symbol values. Table 2 illustrates three example binarization schemes for finite sets of 8
values. Binarization schemes for finite sets can be derived from the universal binarization
schemes for countable infinite sets by modifying some sequences of bins in a way that the
finite sets of bin sequences represent a redundancy-free code (and potentially reordering
the bin sequences). As an example, the truncated unary binarization scheme in Table 2 was
created by modifying the bin sequence for the source symbol 7 of the universal unary
binarization (see Table 1). The truncated and reordered Exp-Golomb binarization of
order 0 in Table 2 was created by modifying the bin sequence for the source symbol 7 of
the universal Exp-Golomb order 0 binarization (see Table 1) and by reordering the bin
sequences (the truncated bin sequence for symbol 7 was assigned to symbol 1). For finite
sets of symbols, it is also possible to use non-systematic / non-universal binarization
schemes, as exemplified in the last column of Table 2.



Each bin 3 of the sequence of bins created by the binarizer 2 is fed into the parameter
assigner4 in sequential order. The parameter assigner assigns a set of one or more
parameters to each bin 3 and outputs the bin with the associated set of parameters 5. The
set of parameters is determined in exactly the same way at encoder and decoder. The set of
parameters may consist of one or more of the following parameters:
- a measure for an estimate of the probability for one of the two possible bin values for
the current bin,
- a measure for an estimate of the probability for the less probable or more probable bin
value for the current bin,
- an identifier specifying an estimate for which of the two possible bin values represents
the less probable or more probable bin value for the current bin,
- the category of the associated source symbol,
- a measure for the importance of the associated source symbol,
- a measure for the location of the associated symbol (e.g. in temporal, spatial, or
volumetric data sets),
- an identifier specifying the channel code protection for the bin or the associated source
symbol,
- an identifier specifying the encryption scheme for the bin or the associated source
symbol,
- an identifier specifying a class for the associated symbol,
- the bin number in the sequence of bins for the associated source symbol.
In an embodiment, the parameter assigner 4 associates each bin 3,5 with a measure for an
estimate of the probability for one of the two possible bin values for the current bin. The
parameter assigner 4 associates each bin 3,5 with a measure for an estimate of the
probability for the less probable or more probable bin value for the current bin and an
identifier specifying an estimate for which of the two possible bin values represents the
less probable or more probable bin value for the current bin. It should be noted that the
probability for the less probable or more probable bin value and the identifier specifying

which of the two possible bin values represents the less probable or more probable bin
value are equivalent measures for the probability of one of the two possible bin values.
In a further embodiment, the parameter assigner 4 associates each bin 3,5 with a measure
for an estimate of the probability for one of the two possible bin values for the current bin
and one or more further parameters (which may be one or more of the above listed
parameters). In a further embodiment, the parameter assigner 4 associates each bin 3,5 with
a measure for an estimate of the probability for the less probable or more probable bin
value for the current bin, an identifier specifying an estimate for which of the two possible
bin values represents the less probable or more probable bin value for the current bin, and
one or more further parameters (which may be one or more of the above listed parameters).
In an embodiment, the parameter assigner 4 determines one or more of the above
mentioned probability measures (measure for an estimate of the probability for one of the
two possible bin values for the current bin, measure for an estimate of the probability for
the less probable or more probable bin value for the current bin, identifier specifying an
estimate for which of the two possible bin values represents the less probable or more
probable bin value for the current bin) based on a set of one or more already encoded
symbols. The encoded symbols that are used for determining the probability measures can
include one or more already encoded symbols of the same symbol category, one or more
already encoded symbols of the same symbol category that correspond to data sets (such as
blocks or groups of samples) of neighboring spatial and/or temporal locations (in relation
to the data set associated with the current source symbol), or one or more already encoded
symbols of different symbol categories that correspond to data sets of the same and/or
neighboring spatial and/or temporal locations (in relation to the data set associated with the
current source symbol).
Each bin with an associated set of parameters 5 that is output of the parameter assigner 4 is
fed into a bin buffer selector 6. The bin buffer selector 6 potentially modifies the value of
the input bin 5 based on the input bin value and the associated parameters 5 and feds the
output bin 7 - with a potentially modified value - into one of two or more bin buffers 8.
The bin buffer 8 to which the output bin 7 is sent is determined based on the value of the
input bin 5 and/or the value of the associated parameters 5.
In an embodiment, the bin buffer selector 6 does not modify the value of the bin, i.e., the
output bin 7 has always the same value as the input bin 5.
In a further embodiment, the bin buffer selector 6 determines the output bin value 7 based

on the input bin value 5 and the associated measure for an estimate of the probability for
one of the two possible bin values for the current bin. In an embodiment, the output bin
value 7 is set equal to the input bin value 5 if the measure for the probability for one of the
two possible bin values for the current bin is less than (or less than or equal to) a particular
threshold; if the measure for the probability for one of the two possible bin values for the
current bin is greater than or equal to (or greater than) a particular threshold, the output bin
value 7 is modified (i.e., it is set to the opposite of the input bin value). In a further
embodiment, the output bin value 7 is set equal to the input bin value 5 if the measure for
the probability for one of the two possible bin values for the current bin is greater than (or
greater than or equal to) a particular threshold; if the measure for the probability for one of
the two possible bin values for the current bin is less than or equal to (or less than) a
particular threshold, the output bin value 7 is modified (i.e., it is set to the opposite of the
input bin value). In an embodiment, the value of the threshold corresponds to a value of 0.5
for the estimated probability for both possible bin values.
The bin buffer selector 6 may determine the output bin value 7 based on the input bin
value 5 and the associated identifier specifying an estimate for which of the two possible
bin values represents the less probable or more probable bin value for the current bin. In an
embodiment, the output bin value 7 is set equal to the input bin value 5 if the identifier
specifies that the first of the two possible bin values represents the less probable (or more
probable) bin value for the current bin, and the output bin value 7 is modified (i.e., it is set
to the opposite of the input bin value) if identifier specifies that the second of the two
possible bin values represents the less probable (or more probable) bin value for the current
bin.
The bin buffer selector 6 may determine the bin buffer 8 to which the output bin 7 is sent
based on the associated measure for an estimate of the probability for one of the two
possible bin values for the current bin. In an embodiment, the set of possible values for the
measure for an estimate of the probability for one of the two possible bin values is finite
and the bin buffer selector 6 contains a table that associates exactly one bin buffer 8 with
each possible value for the estimate of the probability for one of the two possible bin
values, where different values for the measure for an estimate of the probability for one of
the two possible bin values can be associated with the same bin buffer 8. In a further
embodiment, the range of possible values for the measure for an estimate of the probability
for one of the two possible bin values is partitioned into a number of intervals, the bin
buffer selector 6 determines the interval index for the current measure for an estimate of
the probability for one of the two possible bin values, and the bin buffer selector 6 contains
a table that associates exactly one bin buffer 8 with each possible value for the interval

index, where different values for the interval index can be associated with the same bin
buffer 8. In a preferred embodiment, input bins 5 with opposite measures for an estimate of
the probability for one of the two possible bin values (opposite measure are those which
represent probability estimates P and 1 - P) are fed into the same bin buffer 8. In a further
preferred embodiment, the association of the measure for an estimate of the probability for
one of the two possible bin values for the current bin with a particular bin buffer is adapted
over time, e.g. in order to ensure that the created partial bitstreams have similar bit rates.
The bin buffer selector 6 may determine the bin buffer 8 to which the output bin 7 is sent
based on the associated measure for an estimate of the probability for the less probable or
more probable bin value for the current bin. In a preferred embodiment, the set of possible
values for the measure for an estimate of the probability for the less probable or more
probable bin value is finite and the bin buffer selector 6 contains a table that associates
exactly one bin buffer 8 with each possible value of the estimate of the probability for the
less probable or more probable bin value, where different values for the measure for an
estimate of the probability for the less probable or more probable bin value can be
associated with the same bin buffer 8. In a further embodiment, the range of possible
values for the measure for an estimate of the probability for the less probable or more
probable bin value is partitioned into a number of intervals, the bin buffer selector 6
determines the interval index for the current measure for an estimate of the probability for
the less probable or more probable bin value, and the bin buffer selector 6 contains a table
that associates exactly one bin buffer 8 with each possible value for the interval index,
where different values for the interval index can be associated with the same bin buffer 8.
In a further embodiment, the association of the measure for an estimate of the probability
for the less probable or more probable bin value for the current bin with a particular bin
buffer is adapted over time, e.g. in order to ensure that the created partial bitstreams have
similar bit rates.
Each of the two or more bin buffers 8 is connected with exactly one bin encoder 10 and
each bin encoder is only connected with one bin buffer 8. Each bin encoder 10 reads bins
from the associated bin buffer 8 and converts a sequence of bins 9 into a codeword 11,
which represents a sequence of bits. The bin buffers 8 represent first-in-first-out buffers;
bins that are fed later (in sequential order) into a bin buffer 8 are not encoded before bins
that are fed earlier (in sequential order) into the bin buffer. The codewords 11 that are
output of a particular bin encoder 10 are written to a particular partial bitstream 12. The
overall encoding algorithm converts source symbols 1 into two or more partial
bitstreams 12, where the number of partial bitstreams is equal to the number of bin buffers
and bin encoders. In a preferred embodiment, a bin encoder 10 converts a variable number

of bins 9 into a codeword 11 of a variable number of bits. One advantage of the above- and
below-outlined PIPE coding embodiments is that the encoding of bins can be done in
parallel (e.g. for different groups of probability measures), which reduces the processing
time for several implementations.
Another advantage of PIPE coding is that the bin encoding, which is done by the bin
encoders 10, can be specifically designed for different sets of parameters 5. In particular,
the bin encoding and encoding can be optimized (in terms of coding efficiency and/or
complexity) for different groups of estimated probabilities. On the one hand side, this
allows a reduction of the encoding/decoding complexity relative to arithmetic coding
algorithms with similar coding efficiency. On the other hand side, it allows an
improvement of the coding efficiency relative to VLC coding algorithms with similar
encoding/decoding complexity. In an embodiment, the bin encoders 10 implement
different encoding algorithms (i.e. mapping of bin sequences onto codewords) for different
groups of measures for an estimate of the probability for one of the two possible bin
values 5 for the current bin. In a further embodiment, the bin encoders 10 implement
different encoding algorithms for different groups of measures for an estimate of the
probability for the less probable or more probable bin value for the current bin. In a further
embodiment, the bin encoders 10 implement different encoding algorithms for different
channel protection codes. In a further embodiment, the bin encoders 10 implement
different encoding algorithms for different encryption schemes. In a further embodiment,
the bin encoders 10 implement different encoding algorithms for different combinations of
channel protection codes and groups of measures for an estimate of the probability for one
of the two possible bin values 5 for the current bin. In a further embodiment, the bin
encoders 10 implement different encoding algorithms for different combinations of
channel protection codes and groups of measures for an estimate of the probability for the
less probable or more probable bin value 5 for the current bin. In a further embodiment, the
bin encoders 10 implement different encoding algorithms for different combinations of
encryption schemes and groups of measures for an estimate of the probability for one of
the two possible bin values 5 for the current bin. In a further preferred embodiment, the bin
encoders 10 implement different encoding algorithms for different combinations of
encryption schemes and groups of measures for an estimate of the probability for the less
probable or more probable bin value 5 for the current bin.
The bin encoders 10 - or one or more of the bin encoders - may represent binary
arithmetic encoding engines. In a further embodiment, one or more of the bin encoders
represent a binary arithmetic coding engine, wherein the mapping from the representative
LPS/LPB probability PLPS of a given bin buffer to a corresponding code interval width RLPS

- i.e. the interval subdivision of the internal state of the binary arithmetic coding engine,
which is defined by the current interval width R and the current interval offset L,
identifying, for example, the lower bound of the code interval - is realized by using a table
lookup. In a further preferred embodiment, for each table-based binary arithmetic coding
engine associated to a given bin buffer, K representative interval width values {Q0, ..., QK-
l} are used for representing RLPS with the choice of K and the representative interval width
values {Q0, ..., QK-I} being dependent on the bin buffer. For a choice of K > 1, arithmetic
encoding of a bin may involve the substeps of mapping the current interval width R to a
quantization index q with values in{0, ..., K-1) and performing the interval subdivision by
accessing the corresponding partial interval width value Qq from a lookup table with using
q as an index. For a choice of K = 1, i.e., for the case where only one representative
interval width value Q0 is given, this value Q0 may be chosen as a power of two in order to
allow decoding of multiple MPS/MPB values entering the corresponding bin buffer within
a single renormalization cycle. The resulting codewords of each arithmetic coding engine
may be separately transmitted, packetized, or stored, or they may be interleaved for the
purpose of transmission or storage as described hereinafter.
That is, a binary arithmetic coding engine 10 could perform the following steps in coding
the bins in its bin buffer 8:
1. Receiving valLPS, bin from bin buffer (recall: the respective binary arithmetic coding
engine 10 considered here had been chosen to receive "bin" because (or, in other
words, "bin" was associated with the respective binary arithmetic coding engine 10)
the probability distribution estimate, such as p_state[bin], was associated with that
binaiy arithmetic coding engine 10)
2. Quantization of R:
q_index = Qtab[R>>q] (or some other form of quantization)
3. Determination of RLPS and R:
RLPS = Rtab [q_index] (note that p_state is not mentioned here, as it is fixed for the
binary arithmetic coding engine 10 considered, i.e. p_state[encoder], and Rtab has
stored therein pre-calculated values for p[p_state[encoder]]-Q[q_index]
R = R - RLPS [that is, R is preliminarily pre-updated as if "bin" was MPS]
4. Calculation of the new partial interval:
if(bin=l-valMPS)then
L←L + R
R ← RLPS
5. Renormalization of L and R, writing bits,

wherein
q_index describes the index of a quantization value read out of Qtab,
p_state describes the current state (fixed for the binary arithmetic coding engine
10),
RLPS describes the interval width corresponding to the LPS and
valMPS describes the value of the bit corresponding to the MPS.
Accordingly, a binary arithmetic decoding engine 22 could perform the following steps in
decoding the bins output into bin buffer 20:
1. Receiving request for a bin (recall: the respective binary arithmetic decoding engine
22 considered here had been chosen to decode "bin" because (or, in other words, "bin"
was associated with the respective binary arithmetic decoding engine 22) the
probability distribution estimate, such as p_state[bin], was associated with that binary
arithmetic decoding engine 22)
2. Quantization of R:
q_index = Qtab[R>>q] (or some other form of quantization)
3. Determination of RLPS and R:
RLPS - Rtab [q_index] (note that p_state is not mentioned here, as it is fixed for the
binary arithmetic decoding engine 22 considered, i.e. p_state[encoder], and Rtab has
stored therein pre-calculated values for p[p_state[encoder]].Q[q_index]
R = R - RLPS [that is, R is preliminarily pre-updated as if "bin" was MPS]
4. Determination of bin depending on the position of the partial interval:
if(V≥R)then
bin ← 1 - valMPS (bin is decoded as LPS; bin buffer selector 18 will obtain the
actual bin value by use of this bin information and valMPS)
V←V-R
R ← RLPS
else
bin ← valMPS (bin is decoded as MPS; bin buffer selector 18 will obtain the
actual bin value by use of this bin information and valMPS)
5. Renormalization of R, reading out one bit and updating V,
wherein
q_index describes the index of a quantization value
read out of Qtab,
p_state describes the current state (fixed for the binary arithmetic decoding
engine 22),


The bin encoders 10 - or one or more of the bin encoders - may represent entropy
encoders that directly map sequences of input bins 9 onto codewords 10. Such mappings
can be efficiently implemented and don't require a complex arithmetic coding engine. The
inverse mapping of codewords onto sequences of bins (as done in the decoder) should be
unique in order to guarantee perfect decoding of the input sequence, but the mapping of bin
sequences 9 onto codewords 10 doesn't necessarily need to be unique, i.e., it is possible
that a particular sequence of bins can be mapped onto more than one sequence of
codewords. In an embodiment, the mapping of sequences of input bins 9 onto
codewords 10 is bijective. In a further preferred embodiment, the bin encoders 10 - or one
or more of the bin encoders - represent entropy encoders that directly map variable-length
sequences of input bins 9 onto variable-length codewords 10. In an embodiment, the output
codewords represent redundancy-free codes such as general Huffman codes or canonical
Huffman codes.
Two examples for the bijective mapping of bin sequences to redundancy-free codes are
illustrated in Table 3. In a further embodiment, the output codewords represent redundant
codes suitable for error detection and error recovery. In a further preferred embodiment,
the output codewords represent encryption codes suitable for encrypting the source
symbols.



In a farther embodiment, the bin encoders 10 - or one or more of the bin encoders -
represent entropy encoders that directly map variable-length sequences of input bins 9 onto
fixed-length codewords 10. In a further embodiment, the bin encoders 10 - or one or more
of the bin encoders - represent entropy encoders that directly map fixed-length sequences
of input bins 9 onto variable-length codewords 10.
A PIPE decoder according an embodiment is illustrated in Figure 4. The decoder performs
basically the inverse operations of the encoder of Fig. 3, so that the (previously encoded)
sequence of source symbols 27 is decoded from a set of two or more partial bitstreams 24.
The decoder includes two different process flows: A flow for data requests, which
replicates the data flow of the encoder, and a data flow, which represents the inverse of the
encoder data flow. In the illustration in Fig. 4, the dashed arrows represent the data request
flow, while the solid arrows represent the data flow. The building blocks of the decoder
basically replicate the building blocks of the encoder, but implement the inverse
operations.
The decoding of a source symbol is triggered by a request for a new decoded source
symbol 13 that is sent to the binarizer 14. In an embodiment, each request for a new
decoded source symbol 13 is associated with a category of a set of one or more categories.
The category that is associated with a request for a source symbol is the same as the
category that was associated with the corresponding source symbol during encoding.
The binarizer 14 maps the request for a source symbol 13 into one or more requests for a
bin that are sent to the parameter assigner 16. As final response to a request for a bin that is

sent to the parameter assigner 16 by the binarizer 14, the binarizer 14 receives a decoded
bin 26 from the bin buffer selector 18. The binarizer 14 compares the received sequence of
decoded bins 26 with the bin sequences of a particular binarization scheme for the
requested source symbol and, if the received sequence of decoded bins 26 matches the
binarization of a source symbol, the binarizer empties its bin buffer and outputs the
decoded source symbol as final response to the request for a new decoded symbol. If the
already received sequence of decoded bins does not match any of the bin sequences for the
binarization scheme for the requested source symbol, the binarizer sends another request
for a bin to the parameter assigner until the sequence of decoded bins matches one of the
bin sequences of the binarization scheme for the requested source symbol. For each request
for a source symbol, the decoder uses the same binarization scheme that was used for
encoding the corresponding source symbol. The binarization scheme can be different for
different source symbol categories. The binarization scheme for a particular source symbol
category can depend on the set of possible source symbol values and/or other properties of
the source symbols for the particular category.
The parameter assigner assigns a set of one or more parameters to each request for a bin
and sends the request for a bin with the associated set of parameters to the bin buffer
selector. The set of parameters that are assigned to a requested bin by the parameter
assigner is the same that was assigned to the corresponding bin during encoding. The set of
parameters may consist of one or more of the parameters that are mentioned in the encoder
description.
The parameter assigner 16 may associate each request for a bin with a measure for an
estimate of the probability for one of the two possible bin values for the current requested
bin. In particular, the parameter assigner 16 may associate each request for a bin with a
measure for an estimate of the probability for the less probable or more probable bin value
for the current requested bin and an identifier specifying an estimate for which of the two
possible bin values represents the less probable or more probable bin value for the current
requested bin.
In a further embodiment, the parameter assigner 16 associates each request for a bin 15,17
with a measure for an estimate of the probability for one of the two possible bin values for
the current requested bin and one or more further parameters. In a further preferred
embodiment, the parameter assigner 16 associates each request for a bin 15,17 with a
measure for an estimate of the probability for the less probable or more probable bin value
for the current requested bin, an identifier specifying an estimate for which of the two
possible bin values represents the less probable or more probable bin value for the current

requested bin, and one or more further parameters (which may one or more of the above
listed parameters).
In an embodiment, the parameter assigner 16 determines one or more of the above
mentioned probability measures (measure for an estimate of the probability for one of the
two possible bin values for the current requested bin, measure for an estimate of the
probability for the less probable or more probable bin value for the current requested bin,
identifier specifying an estimate for which of the two possible bin values represents the
less probable or more probable bin value for the current requested bin) based on a set of
one or more already decoded symbols. The determination of the probability measures for a
particular request for a bin replicates the process at the encoder for the corresponding bin.
The decoded symbols that are used for determining the probability measures can include
one or more already decoded symbols of the same symbol category, one or more already
decoded symbols of the same symbol category that correspond to data sets (such as blocks
or groups of samples) of neighboring spatial and/or temporal locations (in relation to the
data set associated with the current request for a source symbol), or one or more already
decoded symbols of different symbol categories that correspond to data sets of the same
and/or neighboring spatial and/or temporal locations (in relation to the data set associated
with the current request for a source symbol).
Each request for a bin with an associated set of parameters 17 that is output of the
parameter assigner 16 is fed into a bin buffer selector 18. Based on the associated set of
parameters 17, the bin buffer selector 18 sends a request for a bin 19 to one of two or more
bin buffers 20 and receives a decoded bin 25 from the selected bin buffer 20. The decoded
input bin 25 is potentially modified and the decoded output bin 26 - with a potentially
modified value - is send to the binarizer 14 as final response to the request for a bin with
an associated set of parameters 17.
The bin buffer 20 to which the request for a bin is forwarded is selected in the same way as
the bin buffer to which the output bin of the bin buffer selector at the encoder side was
sent.
In an embodiment, the bin buffer selector 18 determines the bin buffer 20 to which the
request for a bin 19 is sent based on the associated measure for an estimate of the
probability for one of the two possible bin values for the current requested bin. In an
embodiment, the set of possible values for the measure for an estimate of the probability
for one of the two possible bin values is finite and the bin buffer selector 18 contains a
table that associates exactly one bin buffer 20 with each possible value of the estimate of

the probability for one of the two possible bin values, where different values for the
measure for an estimate of the probability for one of the two possible bin values can be
associated with the same bin buffer 20. In a further embodiment, the range of possible
values for the measure for an estimate of the probability for one of the two possible bin
values is partitioned into a number of intervals, the bin buffer selector 18 determines the
interval index for the current measure for an estimate of the probability for one of the two
possible bin values, and the bin buffer selector 18 contains a table that associates exactly
one bin buffer 20 with each possible value for the interval index, where different values for
the interval index can be associated with the same bin buffer 20. Requests for bins 17 with
opposite measures for an estimate of the probability for one of the two possible bin values
(opposite measure are those which represent probability estimates P and 1 - P) may be
forwarded to the same bin buffer 20. Further, the association of the measure for an estimate
of the probability for one of the two possible bin values for the current bin request with a
particular bin buffer may be adapted over time.
The bin buffer selector 18 may determine the bin buffer 20 to which the request for a
bin 19 is sent based on the associated measure for an estimate of the probability for the less
probable or more probable bin value for the current requested bin. In an embodiment, the
set of possible values for the measure for an estimate of the probability for the less
probable or more probable bin value is finite and the bin buffer selector 18 contains a table
that associates exactly one bin buffer 20 with each possible value of the estimate of the
probability for the less probable or more probable bin value, where different values for the
measure for an estimate of the probability for the less probable or more probable bin value
can be associated with the same bin buffer 20. In an embodiment, the range of possible
values for the measure for an estimate of the probability for the less probable or more
probable bin value is partitioned into a number of intervals, the bin buffer selector 18
determines the interval index for the current measure for an estimate of the probability for
the less probable or more probable bin value, and the bin buffer selector 18 contains a table
that associates exactly one bin buffer 20 with each possible value for the interval index,
where different values for the interval index can be associated with the same bin buffer 20.
In a further preferred embodiment, the association of the measure for an estimate of the
probability for the less probable or more probable bin value for the current bin request with
a particular bin buffer is adapted over time.
After receiving a decoded bin 25 from the selected bin buffer 20, the bin buffer selector 18
potentially modifies the input bin 25 and sends the output bin 26 - with a potentially
modified value - to the binarizer 14. The input/output bin mapping of the bin buffer
selector 18 is the inverse of the input/output bin mapping of the bin buffer selector at the

encoder side.
The bin buffer selector 18 may be configured to not modify the value of the bin, i.e., the
output bin 26 has always the same value as the input bin 25.
The bin buffer selector 18 may determine the output bin value 26 based on the input bin
value 25 and the measure for an estimate of the probability for one of the two possible bin
values for the current requested bin that is associated with the request for a bin 17. In an
embodiment, the output bin value 26 is set equal to the input bin value 25 if the measure
for the probability for one of the two possible bin values for the current bin request is less
than (or less than or equal to) a particular threshold; if the measure for the probability for
one of the two possible bin values for the current bin request is greater than or equal to (or
greater than) a particular threshold, the output bin value 26 is modified (i.e., it is set to the
opposite of the input bin value). In a further embodiment, the output bin value 26 is set
equal to the input bin value 25 if the measure for the probability for one of the two possible
bin values for the current bin request is greater than (or greater than or equal to) a
particular threshold; if the measure for the probability for one of the two possible bin
values for the current bin request is less than or equal to (or less than) a particular
threshold, the output bin value 26 is modified (i.e., it is set to the opposite of the input bin
value). In a preferred embodiment, the value of the threshold corresponds to a value of 0.5
for the estimated probability for both possible bin values.
In a further embodiment, the bin buffer selector 18 determines the output bin value 26
based on the input bin value 25 and the identifier, specifying an estimate for which of the
two possible bin values represents the less probable or more probable bin value for the
current bin request, that is associated with the request for a bin 17. In a preferred
embodiment, the output bin value 26 is set equal to the input bin value 25 if the identifier
specifies that the first of the two possible bin values represents the less probable (or more
probable) bin value for the current bin request, and the output bin value 26 is modified
(i.e., it is set to the opposite of the input bin value) if identifier specifies that the second of
the two possible bin values represents the less probable (or more probable) bin value for
the current bin request.
As described above, the bin buffer selector sends a request for a bin 19 to one of the two or
more bin buffers 20. The bin buffers 20 represent first-in-first-out buffers, which are fed
with sequences of decoded bins 21 from the connected bin decoders 22. As response to a
request for a bin 19 that is sent to a bin buffer 20 from the bin buffer selector 18, the bin
buffer 20 removes the bin of its content that was first fed into the bin buffer 20 and sends it

to the bin buffer selector 18. Bins that are earlier sent to the bin buffer 20 are earlier
removed and sent to the bin buffer selector 18.
Each of the two or more bin buffers 20 is connected with exactly one bin decoder 22 and
each bin decoder is only connected with one bin buffer 20. Each bin decoder 22 reads
codewords 23, which represent sequences of bits, from a separate partial bitstream 24. The
bin decoder converts a codeword 23 into a sequence of bins 21 that is sent to the connected
bin buffer 20. The overall decoding algorithm converts two or more partial bitstreams 24
into a number of decoded source symbols, where the number of partial bitstreams is equal
to the number of bin buffers and bin decoders and the decoding of source symbols is
triggered by requests for new source symbols. In an embodiment, a bin decoder 22
converts codewords 23 of a variable number of bits into a sequence of a variable number of
bins 21. One advantage of above PIPE embodiments is that the decoding of bins from the
two or more partial bitstreams can be done in parallel (e.g. for different groups of
probability measures), which reduces the processing time for several implementations.
Another advantage of above PIPE decoding embodiments is that the bin decoding, which is
done by the bin decoders 22, can be specifically designed for different sets of
parameters 17, In particular, the bin encoding and decoding can be optimized (in terms of
coding efficiency and/or complexity) for different groups of estimated probabilities. On the
one hand side, this allows a reduction of the encoding/decoding complexity relative to
arithmetic coding algorithms with similar coding efficiency. On the other hand side, it
allows an improvement of the coding efficiency relative to VLC coding algorithms with
similar encoding/decoding complexity. In an embodiment, the bin decoders 22 implement
different decoding algorithms (i.e. mapping of bin sequences onto codewords) for different
groups of measures for an estimate of the probability for one of the two possible bin
values 17 for the current bin request. In a further embodiment, the bin decoders 22
implement different decoding algorithms for different groups of measures for an estimate
of the probability for the less probable or more probable bin value for the current requested
bin. In a further embodiment, the bin decoders 22 implement different decoding algorithms
for different channel protection codes. In a further embodiment, the bin decoders 22
implement different decoding algorithms for different encryption schemes. In a further
embodiment, the bin decoders 22 implement different decoding algorithms for different
combinations of channel protection codes and groups of measures for an estimate of the
probability for one of the two possible bin values 17 for the current requested bin. In a
further embodiment, the bin decoders 22 implement different decoding algorithms for
different combinations of channel protection codes and groups of measures for an estimate
of the probability for the less probable or more probable bin value 17 for the current

requested bin. In a further embodiment, the bin decoders 22 implement different decoding
algorithms for different combinations of encryption schemes and groups of measures for an
estimate of the probability for one of the two possible bin values 17 for the current
requested bin. In a further embodiment, the bin decoders 22 implement different decoding
algorithms for different combinations of encryption schemes and groups of measures for an
estimate of the probability for the less probable or more probable bin value 17 for the
current requested bin.
The bin decoders 22 do the inverse mapping of the corresponding bin encoders at the
encoder side.
In an embodiment, the bin decoders 22 - or one or more of the bin decoders - represent
binary arithmetic decoding engines.
In a further embodiment, the bin decoders 22 - or one or more of the bin decoders -
represent entropy decoders that directly map codewords 23 onto sequences of bins 21.
Such mappings can be efficiently implemented and don't require a complex arithmetic
coding engine. The mapping of codewords onto sequences of bins has to be unique. In an
embodiment, the mapping of codewords 23 onto sequences of bins 21 is bijective. In a
further embodiment, the bin decoders 10 - or one or more of the bin decoders - represent
entropy decoders that directly map variable-length codewords 23 into variable-length
sequences of bins 21. In an embodiment, the input codewords represent redundancy-free
codes such as general huffman codes or canonical huffman codes. Two examples for the
bijective mapping of redundancy-free codes to bin sequences are illustrated in Table 3. In a
further embodiment, the input codewords represent redundant codes suitable for error
detection and error recovery. In a further embodiment, the input codewords represent
encryption codes.
The bin decoders 22 - or one or more of the bin decoders - may represent entropy
decoders that directly map fixed-length codewords 23 onto variable-length sequences of
bins 21. Alternatively the bin decoders 22 - or one or more of the bin decoders - represent
entropy decoders that directly map variable-length codewords 23 onto fixed-length
sequences of bins 21.
Thus, Fig. 3 and 4 showed an embodiment for a PIPE encoder for encoding a sequence of
source symbols 1 and a PIPE decoder for reconstructing same. That is, the PIPE encoder of
Fig. 3 may be used as the PIPE encoder 104 in Fig. 1a with binarizer 2 acting as
symbolizer 122, parameter assigner 4 acting as assigner 114, bin buffer selector 6 acting as

selector 120, and the pair of serially connected bin buffer 8 and bin encoder 10 acting as a
respective one of the entropy encoders 116 each of which outputs bitstreams 12
corresponding to bitstreams 118 in Fig. 1a. As becomes clear from the comparison of Fig.
3 and Fig. 1, assigner 114 of Fig. la may have its input alternatively be connected to the
input side of symbolizer 122 rather than the output side of the latter. Similarly, the PIPE
decoder of Fig. 4 may be used as PIPE decoder 202 in Fig. 2a with partial bitstreams 24
corresponding to bitstreams 216 in Fig. 2, the pairs of serially connected buffer 20 and bin
decoder 22 corresponding to the individual entropy decoders 210, bin buffer selector 18
acting as selector 214, parameter assigner 16 acting as assigner 212 and binarizer 14 acting
as desymbolizer 222. Again, a comparison between Fig. 2a and Fig. 4 makes clear that the
interconnection between desymbolizer 222, assigner 212 and selector 214 may be
configured differently, so that, in accordance with an alternative embodiment, the
connections of Fig. 2a are amended to correspond to those shown in Fig. 4.
The PIPE encoder of Fig. 3 comprises an assigner 4 configured to assign a number of
parameters 5 to each alphabet symbol of the sequence of alphabet symbols 3. The
assignment is based on information contained within previous alphabet symbols of the
sequence of alphabet symbols such as the category of the syntax element 1 to the
representation - such as binarization - of which the current alphabet symbol belongs and
which, according to the syntax structure of the syntax elements 1, is currently be expected
which expectation, in turn, is deducible from the history of previous syntax elements 1 and
alphabet symbols 3. Further, the encoder comprises a plurality of entropy encoders 10 each
of which is configured to convert the alphabet symbols 3 forwarded to the respective
entropy encoder into a respective bitstream 12, and a selector 6 configured to forward each
alphabet symbol 3 to a selected one of the plurality of entropy encoders 10, the selection
depending on the number of parameters 5 assigned to the respective alphabet symbol 3.
The PIPE decoder of Fig. 4 comprises a plurality of entropy decoders 22, each of which is
configured to convert a respective bitstream 23 into alphabet symbols 21; an assigner 16
configured to assign a number of parameters 17 to each alphabet symbol 15 of a sequence
of alphabet symbols to be reconstructed based on information contained within previously
reconstructed alphabet symbols of the sequence of alphabet symbols (see 26 and 27 in Fig.
4); and a selector 18 configured to retrieve each alphabet symbol of the sequence of
alphabet symbols to be reconstructed from a selected one of the plurality of entropy
decoders 22, the selection depending on the number of parameters defined to the respective
alphabet symbol. The assigner 16 may be configured such that the number of parameters
assigned to each alphabet symbol comprises, or is, a measure for an estimate of a
probability of distribution among the possible alphabet symbol values a respective alphabet
symbol may assume. The sequence of alphabet symbols to be reconstructed may be of a

binaiy alphabet and the assigner 16 may be configured such that the estimate of the
probability distribution consists of a measure for an estimate of a probability of a less
probable or more probable bin value of the two possible bin values of the binary alphabet
and an identifier specifying an estimate for which of the two possible bin values represents
the less probable or more probable bin value. The assigner 16 may further be configured to
internally assign a context to each alphabet symbol of the sequence of alphabet symbols 15
to be reconstructed based on the information contained within previously reconstructed
alphabet symbols of the sequence of alphabet symbols to be reconstructed with each
context having a respective probability distribution estimate associated therewith, and to
adapt the probability distribution estimate for each context to an actual symbol statistic
based on symbol values of previously reconstructed alphabet symbols to which the
respective context is assigned. The context may take into account a spatial relationship or
neighborhood of positions to which the syntax elements belong such as in video or picture
coding, or even in tables in case of financial applications. Then, the measure for the
estimate of the probability distribution for each alphabet symbol may be determined based
on the probability distribution estimate associated with the context assigned to the
respective alphabet symbol such as by quantizing the probability distribution estimate
associated with the context assigned with the respective alphabet symbol to one of a
plurality of probability distribution estimate representatives in order to obtain the measure
for the estimate of the probability distribution. The selector may be configured such that a
surjective association is defined between the plurality of entropy encoders and the plurality
of probability distribution estimate representatives, i.e. each entropy encoder has at least
one probability distribution estimate representative associated therewith, but more than one
probability distribution estimate representative may be associated with one entropy
encoder. In accordance with an embodiment, the association may even be bijective. The
selector 18 may be configured to change a quantization mapping from a range of the
probability distribution estimates to the plurality of probability distribution estimate
representatives in a predetermined deterministic way depending on previously
reconstructed alphabet symbols of the sequence of alphabet symbols, over time. That is,
selector 18 may change the quantization step sizes, i.e. the intervals of probability
distributions mapped onto the individual probability indices which, in turn, may be
surjectively associated with the individual entropy decoders. The plurality of entropy
decoders 22, in turn, may be configured to adapt their way of converting alphabet symbols
into bit streams responsive to a change in the quantization mapping. For example, each
entropy decoder 22 may be optimized for, i.e. may have an optimal compression rate for, a
certain probability distribution estimate within the respective probability distribution
estimate quantization interval, and may change its codeword/symbol sequence mapping so
as to adapt the position of this certain probability distribution estimate within the

respective probability distribution estimate quantization interval upon a change of the latter
so as to be optimized. The selector may be configured to change the quantization mapping
such that rates by which the alphabet symbols are retrieved from the plurality of entropy
decoders, are made less dispersed. As to the binarizer 14 it is noted that same may be left
away if the syntax elements are already binary. Further, depending on the type of decoder
22, the existence of the buffers 20 is not necessary. Further, the buffers may be integrated
within the decoders.
So far, more detailed embodiments for the PIPE encoder 104 and the PIPE decoder 202 in
Fig. la and 2 have been described above, with respect to Fig. 3 and 4, which, if readily
implemented in the apparatuses of Fig. 1 a and 2, lead to a parallel bitstream output in
which the VLC and PIPE partial bitstreams are conveyed in parallel. In the following,
possibilities are described, how to combine the PIPE partial bitstreams for being, then,
transmitted along VLC bitstream in parallel, or with secondly interleaving both bitstreams,
i.e. the VLC bitstream and the interleaved PIPE bitstream.
Termination of finite source symbol sequences
In an embodiment for the PIPE en-and decoders, the encoding and decoding is done for a
finite set of source symbols. Often a certain quantity of data such as a still image, a frame
or field of a video sequence, a slice of an image, a slice of a frame or a field of a video
sequence, or a set of successive audio samples, etc. is coded. For finite sets of source
symbols, in general, the partial bitstreams that are created at the encoder side have to be
terminated, i.e., it has to be ensured that all source symbols can be decoded from the
transmitted or stored partial bitstreams. After the last bin is inserted into the corresponding
bin buffer 8, the bin encoder 10 has to ensure that a complete codeword is written to the
partial bitstream 12. If the bin encoder 10 represents a binary arithmetic coding engine, the
arithmetic codeword has to be terminated. If the bin encoder 10 represents an entropy
encoder that implements a direct mapping of bin sequences onto codewords, the bin
sequence that is stored in the bin buffer after writing the last bin to the bin buffer might not
represent a bin sequence that is associated with a codeword (i.e., it might represent a prefix
of two or more bin sequences that are associated with codewords). In such a case, any of
the codewords associated with a bin sequence that contains the bin sequence in the bin
buffer as prefix has to be written to the partial bitstream (the bin buffer has to be flushed).
This could be done by inserting bins with a particular or an arbitrary value into the bin
buffer until a codeword is written. In a preferred embodiment, the bin encoder selects one
of the codewords with minimum length (in addition to the property that the associated bin
sequence must contain the bin sequence in the bin buffer as prefix). At the decoder side,

the bin decoder 22 may decode more bins than required for the last codeword in a partial
bitstream; these bins are not requested by the bin buffer selector 18 and are discarded and
ignored. The decoding of the finite set of symbols is controlled by requests for decoded
source symbols; if no further source symbol is requested for a quantity of data, the
decoding is terminated.
Transmission and multiplexing of the partial bitstreams
The partial bitstreams 12 that are created by the PIPE encoder can be transmitted
separately, or they can be multiplexed into a single bitstream, or the codewords of the
partial bitstreams can be interleaved in a single bitstream.
In an embodiment, each partial bitstream for a quantity of data is written to one data
packet. The quantity of data can be an arbitrary set of source symbols such as a still
picture, a field or frame of a video sequence, a slice of a still picture, a slice of a field or
frame of a video sequence, or a frame of audio samples, etc.
In another preferred embodiment, two or more of the partial bitstreams for a quantity of
data or all partial bitstreams for a quantity of data are multiplexed into one data packet.
The structure of a data packet that contains multiplexed partial bitstreams is illustrated in
Figure 5. That is, the data packet shown in Fig. 5 could be part of the intermediate
interleaved stream 132 and 234, respectively.
The data packet 300 consists of a header and one partition for the data of each partial
bitstream (for the considered quantity of data). The header 300 of the data packet contains
indications for the partitioning of the (remainder of the) data packet into segments of
bitstream data 302. Beside the indications for the partitioning, the header may contain
additional information. In an embodiment, the indications for the partitioning of the data
packet are the locations of the beginning of the data segments in units of bits or bytes or
multiples of bits or multiples of bytes. In an embodiment, the locations of the beginning of
the data segments are coded as absolute values in the header of the data packet, either
relative to the beginning of the data packet or relative to the end of the header or relative to
the beginning of the previous data packet. In a further embodiment, the locations of the
beginning of the data segments are differentially coded, i.e., only the difference between
the actual beginning of a data segment and a prediction for the beginning of the data
segment is coded. The prediction can be derived based on already known or transmitted
information such as the overall size of the data packet, the size of the header, the number
of data segments in the data packet, the location of the beginning of preceding data

segments. In an embodiment, the location of the beginning of the first data packet is not
coded, but inferred based on the size of the data packet header. At the decoder side, the
transmitted partition indications are used for deriving the beginning of the data segments.
The data segments are then used as partial bitstreams and the data contained in the data
segments are fed into the corresponding bin decoders in sequential order.
There are several alternatives for multiplexing the partial bitstreams 12 into a data packet.
One alternative, which can reduce the require side information, in particular for cases in
which the sizes of the partial bitstreams are very similar, is illustrated in Fig. 6. The
payload of the data packet, i.e., the data packet 310 without its header 311, is partitioned
into segments 312a predefined way. As an example, the data packet payload can be
partitioned into segments of the same size. Then each segment is associated with a partial
bitstream or with the first part of a partial bitstream 313. If a partial bitstream is greater
than the associated data segment, its remainder 314 is placed into the unused space at the
end of other data segments. This can be done in a way that the remaining part of a
bitstream is inserted in reverse order (starting from the end of the data segment), which
reduces the side information. The association of the remainders of the partial bitstreams to
data segments and, when more than one remainder is added to a data segment, the start
point for one or more of the remainders have to be signaled inside the bitstream, e.g. in the
data packet header.
Interleaving of variable-length codewords
For some applications, the above described multiplexing of the partial bitstreams 12 (for a
quantity of source symbols) in one data packet can have the following disadvantages: On
the one hand side, for small data packets, the number of bits for the side information that is
required for signaling the partitioning can become significant relative to the actual data in
the partial bitstreams, which finally reduces the coding efficiency. On the other hand, the
multiplexing may not suitable for applications that require a low delay (e.g. for video
conferencing applications). With the described multiplexing, the PIPE encoder cannot start
the transmission of a data packet before the partial bitstreams have been completely
created, since the locations of the beginning of the partitions are not known before.
Furthermore, in general, the PIPE decoder has to wait until it receives the beginning of the
last data segment before it can start the decoding of a data packet. For applications as video
conferencing systems, these delays can add-up to an additional overall delay of the system
of several video pictures (in particular for bit rates that are close to the transmission bit rate
and for encoders/decoders that require nearly the time interval between two pictures for
encoding/decoding a picture), which is critical for such applications. In order to overcome

the disadvantages for certain applications, the PIPE encoder can be configured in a way
that the codewords that are generated by the two or more bin encoders are interleaved into
a single bitstream. The bitstream with the interleaved codewords can be directly send to the
decoder (when neglecting a small buffer delay, see below). At the PIPE decoder side, the
two or more bin decoders read the codewords directly from the bitstream in decoding
order; the decoding can be started with the first received bit. In addition, no side
information is required for signaling the multiplexing (or interleaving) of the partial
bitstreams.
The basic structure of a PIPE encoder with codeword interleaving is shown in Fig. 7. The
bin encoders 10 don't write the codewords directly to the partial bitstreams, but are
connected with a single codeword buffer 29, from which codewords are written to the
bitstream 34 in coding order. The bin encoders 10 send requests for one or more new
codeword buffer entries 28 to the codeword buffer 29 and later send the codewords 30 to
the codeword buffer 29, which are stored in the reserved buffer entries. The (in general
variable-length) codewords 31 of the codeword buffer 29 are accessed by a codeword
writer 32, which writes the corresponding bits 33 to the produced bitstream 34. The
codeword buffer 29 operates as a first-in-first-out buffer; codeword entries that are
reserved earlier are earlier written to the bitstream.
In a further generalization, multiple codeword buffers and partial bitstreams 12 are
possible, where the number of codeword buffers is less than the number of bin encoders. A
bin encoder 10 reserves one or more codewords in the codeword buffer 29, whereby the
reservation of the one or more codewords in the codeword buffer is triggered by certain
events in the connected bin buffer 8. In an embodiment, the codeword buffer 29 is operated
in a way that the PIPE decoder can instantaneously decode the bitstream 34 which
corresponds to 132 in Fig. 1a and 134 in Fig. 2, respectively. The coding order in which
the codewords are written to the bitstream is the same as the order in which the
corresponding codewords are reserved in the codeword buffer. In an embodiment, each bin
encoder 10 reserves one codeword, with the reservation being triggered by a certain event
in the connected bin buffer. In another embodiment, each bin encoder 10 reserves more
than one codeword, with the reservation being triggered by a certain event in the connected
bin buffer. In further embodiment, the bin encoders 10 reserve a different amount of
codewords, where the amount of codewords that are reserved by a particular bin encoder
can be dependent on the particular bin encoder and/or other properties of the particular bin
encoder/bin buffer (such as the associated probability measure, the number of already
written bits, etc.).

In an embodiment, the codeword buffer is operated as follows. If a new bin 7 is sent to a
particular bin buffer 8 and the number of already stored bins in the bin buffer is zero and
there is currently no codeword reserved in the codeword buffer for the bin encoder that is
connected with the particular bin buffer, the connected bin encoder 10 sends a request to
the codeword buffer, by which one or more codeword entries are reserved in the codeword
buffer 29 for the particular bin encoder. The codeword entries can have a variable number
of bits; an upper threshold for the number of bits in a buffer entry is usually given by the
maximum codeword size for the corresponding bin encoder. The next codeword or the next
codewords that are produced by the bin encoder (for which the codeword entry or
codeword entries have been reserved) are stored in the reserved entry or entries of the
codeword buffer. If all reserved buffer entries in the codeword buffer for a particular bin
encoder are filled with codewords and the next bin is sent to the bin buffer that is
connected with the particular bin encoder, one or more new codewords are reserved in the
codeword buffer for the particular bin encoder, etc. The codeword buffer 29 represents a
first-in-first-out buffer in a certain way. Buffer entries are reserved in sequential order.
Codewords for which the corresponding buffer entries have been reserved earlier are
earlier written to the bitstream. The codeword writer 32 checks the status of the codeword
buffer 29, either continuously or after a codeword 30 is written to the codeword buffer 29.
If the first buffer entry contains a complete codeword (i.e., the buffer entry is not reserved,
but includes a codeword), the corresponding codeword 31 and the corresponding buffer
entry are removed from the codeword buffer 20 and the bits of the codeword 33 are written
to the bitstream. This process is repeated until the first buffer entry does not contain a
codeword (i.e., it is reserved or free). At the end of the decoding process, i.e., if all source
symbols of the considered quantity of data have been processed, the codeword buffer must
be flushed. For that flushing process, the following is applied for each bin buffer/ bin
encoder as first step: If the bin buffer does contain bins, a bin with a particular or an
arbitrary value is added until the resulting bin sequence represents a bin sequence that is
associated with a codeword (as noted above, one preferred way of adding bins is to add
such bin values that produce the shortest possible codeword - or one of those - that is
associated with a bin sequence that contains the for the original content of the bin buffer as
prefix), then the codeword is written to the next reserved buffer entry for the corresponding
bin encoder (and the corresponding) bin buffer is emptied. If more than one buffer entry
has been reserved for one or more bin encoders, the codeword buffer may still contain
reserved codeword entries. In that case, these codeword entries are filled with arbitrary, but
valid codewords for the corresponding bin encoders. In a preferred embodiment, the
shortest valid codeword or one of the shortest valid codewords (if there are multiple) is
inserted. Finally, all remaining codewords in the codeword buffer are written to the
bitstream.

Two examples for the status of the codeword buffer are illustrated in Fig. 8. In
example (a), the codeword buffer contains 2 entries that are filled with a codeword and 5
reserved entries. In addition, the next free buffer entry is marked. The first entry is filled
with a codeword (i.e., the bin encoder 2 just wrote a codeword to a previously reserved
entry). In the next step, this codeword will be removed from the codeword buffer and
written to the bitstream. Then, the first reserved codeword for bin encoder 3 is the first
buffer entry, but this entry cannot be removed from the codeword buffer, since it is only
reserved, but no codeword has been written to this entry. In the example (b), the codeword
buffer contains 3 entries that are filled with a codeword and 4 reserved entries. The first
entry is marked as reserved and hence the codeword writer cannot write a codeword to the
bitstream. Although 3 codewords are contained in the codeword buffer, the codeword
writer has to wait until a codeword is written to the first reserved buffer entry for bin
encoder 3. Note that the codewords must be written in the order in which they were
reserved, in order to be able to invert the process at the decoder side (see below).
The basic structure of a PIPE decoder with codeword interleaving is shown in Fig. 9. The
bin decoders 10 don't read the codewords directly from separate partial bitstreams, but are
connected to a bit buffer 38, from which the codewords 37 are read in coding order. It
should be noted that the bit buffer 38 is not necessarily required, since the codewords could
also be directly read from the bitstream. The bit buffer 38 is mainly included in the
illustration for clearly separate different aspects of the processing chain. The bits 39 of the
bitstream 40 with interleaved codewords, which thus corresponds to bitstream 234 in Fig.
2, are sequentially inserted into the bit buffer 38, which represents a first-in-first-out
buffer. If a particular bin decoder 22 receives a request for one or more bin sequences 35,
the bin decoder 22 reads one or more codewords 37 from the bit buffer 38 via requests for
bits 36. The PIPE decoder can instantaneously decode the source symbols. Note that the
PIPE encoder (as described above) must ensure by suitably operating the codeword buffer
that the codewords are written in the same order to the bitstream in which they are
requested by the bin decoders. At the PIPE decoder, the entire decoding process is
triggered by requests for source symbols. Parameters as the number of codewords that are
reserved at the encoder side by a particular bin encoder and the number of codewords that
are read by the corresponding bin decoder must be the same.
In a further generalization, multiple codeword buffers and partial bitstreams are possible,
where the number of bit buffers is less than the number of bin decoders. A bin decoder 22
reads one or more codewords from the bit buffer 38 at one time instant, whereby the
reading of the one or more codewords from the bit buffer is triggered by certain events in

the connected bin buffer 20. In an embodiment, the decoder is operated in a way that one
or more codewords are read when a request for a bin 19 is sent to a particular bin buffer 20
and the bin buffer doesn't contain any bins. But it is also possible to trigger the reading of
codewords by other events, e.g. if the number of bins in the bin buffer is below a
predefined threshold. In an embodiment, each bin decoder 22 reads one codeword, with the
reading being triggered by a certain event in the connected bin buffer. In another
embodiment, each bin decoder 22 reads more than one codeword, with the reading being
triggered by a certain event in the connected bin buffer. In a further embodiment, the bin
decoders 22 read a different amount of codewords, where the amount of codewords that
are read by a particular bin decoder can be dependent on the particular bin decoder and/or
other properties of the particular bin decoder/bin buffer (such as the associated probability
measure, the number of already read bits, etc.).
In an embodiment, the reading of codewords from the bit buffer is operated as follows. If a
new bin request 19 is sent from the bin buffer selector 18 to a particular bin buffer 20 and
the number of bins in the bin buffer is zero, the connected bin decoder 22 reads one or
more codewords 37 from the bit buffer 38, via bit request 36 to the bit buffer 38. The bin
decoder 22 converts the read codewords 37 into sequences of bins 21 and stores these bin
sequences in the connected bin buffer 20. As final response to the request for a bin 19, the
first inserted bin is removed from the bin buffer 20 and sent to the bin buffer selector 18.
As response the further bin requests, the remaining bins in the bin buffer are removed until
the bin buffer is empty. An additional bin request triggers the bin decoder to read one or
more new codewords from the bit buffer, etc. The bit buffer 38 represents a first-in-first-
out buffer of a predefined size and is continuously filled with bits 39 from the bitstream 40.
In order to ensure that the codewords are written to the bitstream in the same way as they
are requested by the decoding process, the codeword buffer at the encoder side can be
operated in the way described above.
Thus, each of the plurality of entropy decoders may be a variable length decoder
configured to map codewords of fixed lengths to symbol sequences of variable lengths, and
a codeword entry such as the output of the codeword buffer 43 may be provided for
receiving a single stream of interleaved codewords. The plurality of entropy decoders 22
may be configured to retrieve the codewords from the codeword entry in a sequential order
depending on an order in which the symbols of the sequence of symbols to be
reconstructed as retrieved by the selector 18 from the plurality of entropy decoders result in
a new symbol sequence to be mapped from a new codeword at the respective entropy
decoders.

Interleaving of variable-length codewords with a low-delay constraint
The described codeword interleaving for the PIPE coding does not require that any
partitioning information is sent as side information. And since the codewords are
interleaved in the bitstream, the delay is in general small. However, it is not guaranteed
that a particular delay constraint (e.g. specified by a maximum number of bits that are
stored in the codeword buffer) is obeyed. Furthermore, the required buffer size for the
codeword buffer can theoretically become very large. When considering the example in
Fig. 8(b), it might be possible that no further bins are send to bin buffer 3 and hence the bin
encoder 3 will not send any new codeword to the codeword buffer until the flushing
process at the end of the data packet is applied. Then all codewords for bin encoders 1
and 2 would have to wait until the end of the data packet, before they can be written to the
bitstream. This drawback can be circumvented by adding a further mechanism to the PIPE
encoding process (and also to the PIPE decoding process as described later). The basic
concept of that additional mechanism is that if a measure related to the delay or an upper
bound of the delay (see below) exceeds a specified threshold, the first reserved buffer entry
is filled by flushing the corresponding bin buffer (using a similar mechanism as at the end
of a data packet). By such a mechanism, the number of waiting buffer entries is reduced
until the associated delay measure is less than the specified threshold. At the decoder side,
the bins that have been inserted at the encoder side in order to obey the delay constraint
must be discarded. For this discarding of bins basically the same mechanism as at the
encoder side can be used. In the following two embodiments for such a delay control are
described.
In one embodiment, the measure for the delay (or an upper bound of the delay) is the
number of active buffer entries in the codeword buffer, where the number of active buffer
entries is the number of reserved buffer entries plus the number of buffer entries that
contain codewords. Note that the first buffer entry is always a reserved buffer entry or a
free buffer entry, since if the first buffer entry contains a codeword, this codeword is
written to the bitstream. If for example, the maximum allowed buffer delay (as determined
by the application) is D bits and the maximum codeword size for all bin encoders is L, a
lower bound for the maximum number of codewords that can be contained in the codeword
buffer without violating the delay constraint can be calculated by N = D/L. The delay
measure D in bits is not required by the system, but the maximum number of codewords TV
must be known to both encoder and decoder. In an embodiment, the maximum number of
codeword buffer entries N is fixed by the application. In another embodiment, the
maximum number of codeword buffer entries N is signaled inside the bitstream, e.g., in the
header of the data packet (or slice header) or in a parameter set, which is included in the

bitstream. If a bin encoder 10 sends a request for the reservation of one or more new buffer
entries to the codeword buffer 29, the following process is executed before a new
codeword buffer entry is reserved (i.e., it is executed multiple times if multiple codeword
buffer entries are reserved by one request): If the number of currently active buffer entries
plus 1 (taking into account the buffer entry that will be reserved next) is greater than the
maximum number of codeword buffer entries N, the first buffer entry (which is reserved) is
flushed by the process described in the following until the number of currently active
buffer entries plus 1 is less than or equal to the maximum number of codeword buffer
entries N. The flushing of a reserved buffer entry is similar to the flushing at the end of a
data packet: The bin encoder 10 that has reserved the corresponding first buffer entry is
flushed by adding bins with particular or arbitrary values to the connected bin buffer 8
until the resulting bin sequence represents a bin sequence that is associated with a
codeword, the codeword is then written to the reserved buffer entry and it is finally added
to the bitstream (while emptying the bin buffer and removing the previously reserved
buffer entry). As mentioned above, one preferred way for adding bins to the bin buffer is to
add those bins that produce the shortest possible codeword. At the decoder side, a similar
process is executed for discarding the bins that have been added to obey the delay
constraint. Therefore, the decoder maintains a counter C that counts the codewords that
have been read from the bit buffer (this counter can be maintained in the bit buffer). This
counter C is initialized (e.g. with zero) at the beginning of the decoding of a data packet
and is increased by one after a codeword is read. In addition, each bin decoder 22 contains
a counter Cx, which stores the value of the codeword counter C before the last codeword
was read by the corresponding bin decoder 22. I.e., when a particular bin decoder 22 reads
a new codeword, its counter Cx is set equal to C as a first step and then the codeword is
read from the bit buffer. When a request for a bin 19 is sent to a particular bin buffer 20
and the difference (C - Cx) between the overall codeword counter C and the counter Cx of
the connected bin decoder 22 is greater than the maximum number of codeword buffer
entries N, all bins that are currently stored in the particular bin buffer 20 are discarded and
ignored. Beside that additional step, the decoding is operated as described above. If the bin
buffer 20 to which a request for a bin 19 is sent is empty (either because all bins have
already been removed or because the low-delay mechanism did discard all bins in the first
step after the bin request has been received), the connected bin decoder 22 reads one or
more new codewords from the bit buffer 38 etc.
In another embodiment, the measure for the delay (or an upper bound of the delay) is the
sum of the maximum codeword lengths for the active buffer entries in the codeword
buffer, where the maximum codeword length for a particular buffer entry depends on the
bin decoded that is associated with that buffer entry. As illustration, the maximum

codeword lengths for the buffer entries are indicated in the examples in 6, Note again that
the first buffer entry is always a reserved buffer entry or a free buffer entry, since if the
first buffer entry contains a codeword, this codeword is written to the bitstream. Let the
maximum allowed buffer delay (as determined by the application) be D bits. This
maximum buffer delay D must be known to both encoder and decoder. In a preferred
embodiment, the maximum buffer delay D is fixed by the application. In another preferred
embodiment, the maximum buffer delay D is signaled inside the bitstream, e.g., in the
header of the data packet (or slice header) or in a parameter set, which is included in the
bitstream. It can be signaled in units of bits, or bytes, or a multiple of bits, or a multiple of
bytes. If a bin encoder 10 sends a request for the reservation of one or more new buffer
entries to the codeword buffer 29, the following process is executed before a new
codeword buffer entry is reserved (i.e., it is executed multiple times if multiple codeword
buffer entries are reserved by one request).
If the sum of the maximum codeword lengths for all currently active buffer entries plus the
maximum codeword length for the buffer entry that will be reserved is greater than the
maximum buffer delay D, the first buffer entry (which is reserved) is flushed by the
process described above until the sum of the maximum codeword lengths for all active
buffer entries plus the maximum codeword length for the buffer entry that will be reserved
is less than or equal to the maximum buffer delay D. As an example, let's consider the
example in Fig. 8(b). The sum of the maximum codeword lengths for all currently active
buffer entries is 29. Let's assume that the maximum buffer delay D is set equal to 32. If the
next buffer entry is reserved by bin encoder 2 for which the maximum codeword length is
equal to 3, the first buffer entry is not flushed, since 29 + 3 is not greater than 32. But if the
next buffer entry is reserved by bin encoder 1 for which the maximum codeword length is
equal to 7, the first buffer entry is flushed, since 29 + 7 is greater than 32. The flushing of
the reserved buffer entry is done as described above (by adding bin with particular or
arbitrary values to the corresponding bin buffer).
At the decoder side, a similar process is executed for discarding the bins that have been
added to obey the delay constraint. Therefore, the decoder maintains a counter C that
counts the maximum codeword length for the codewords that have been read from the bit
buffer (this counter can be maintained in the bit buffer). Note that the maximum codeword
lengths that are associated with different bin decoders can be different. The counter C is
initialized (e.g. with zero) at the beginning of the decoding of a data packet and it is
increased after a codeword is read. This counter is not increased by the actual length of the
read codewords, but by its maximum length. I.e., if a codeword is read by a particular bin
decoder and the maximum codeword length that is associated with the codeword table used

by the particular bin decoder is Lx (a different bin decoder can be associated with a
different maximum codeword length), the counter C is increased by Lx. In addition to the
overall counter C, each bin decoder 22 contains a counter Cx, which stores the value of the
codeword counter C before the last codeword was read by the corresponding bin
decoder 22. I.e., when a particular bin decoder 22 reads a new codeword, its counter Cx is
set equal to C as a first step and then the codeword is read from the bit buffer. When a
request for a bin 19 is sent to a particular bin buffer 20 and the difference (C - Cx)
between the overall counter C and the counter Cx of the connected bin decoder 22 is
greater than the maximum buffer delay D, all bins that are currently stored in the particular
bin buffer 20 are discarded and ignored. Beside that additional step, the decoding is
operated as described above. If the bin buffer 20 to which a request for a bin 19 is sent is
empty (either because all bins have already been removed or because the low-delay
mechanism did discard all bins in the first step after the bin request has been received), the
connected bin decoder 22 reads one or more new codewords from the bit buffer 38 etc.
Thus, the plurality of entropy decoders 22 and the selector 18 may be configured to
intermittently discard suffixes of symbol sequences so as to not participate in forming the
sequence of symbols to be reconstructed 29. The intermittently discarding may be
performed at events where a number of codewords having been retrieved from the
codeword entry by the plurality of entropy decoders between two consecutive codeword
retrievals of a respective entropy decoder from the codeword entry, fulfils a predetermined
criterion. The plurality of entropy encoders and the codeword buffer may, in turn, be
configured to intermittently extend currently forwarded but not yet mapped symbols to
valid symbol sequences by don't-care symbols having the currently forwarded but not yet
mapped symbols as prefix, map the thus extended symbol sequences into codewords, enter
the thus obtained codewords into the reserved codeword entries and flush the codeword
entries. The intermittently extending, entering and flushing may take place at events where
a number of reserved codeword entries plus a number of codeword entries having
codewords entered therein fulfils a predetermined criterion. The predetermined criteria
may take the maximum lengths of codewords of the plurality of encoder/decoder pairs into
account.
For some architectures, the above described preferred embodiment for the codeword
interleaving might result in a drawback in terms of the decoding complexity. As illustrated
in Fig. 9, all bin decoders 22 read codewords (in the general case, variable-length
codewords) from a single bit buffer 38. The reading of the codewords cannot be done in
parallel, since the codeword must be read in the correct order. That means, a particular bin
decoder must wait until other bin decoders finish the reading of codewords. And when the

complexity of the reading of the variable-length codewords is significant in relation to the
remainder of the (partially parallelized) decoding process, this access of the variable-length
codewords can be a bottleneck for the entire decoding process. There are some variations
of the described embodiments that can be employed for reducing the complexity of the
access from the single bit buffer, a few of them will be described in the following. In one
preferred embodiment, there exists a single set of codewords (representing for instance a
redundancy-free prefix code) and the set of codewords that is used for each bin decoder 22
is a subset of the single codeword set. Note that different bin decoders 22 can use different
subsets of the single codeword set. Even if the codeword sets that are used by some of the
bin decoders 22 are the same, their association with bin sequences is different for different
bin decoders 22. In a particular embodiment, the same set of codewords is used for all bin
decoders 22. If we have a single codeword set that includes the codeword sets for all bin
decoders as subsets, the parsing of the codewords can be done outside the bin decoders,
which can reduce the complexity of the codeword access. The PIPE encoding process is
not changed in relation to the above described process. The modified PIPE decoding
process is illustrated in Fig. 10. A single codeword reader is fed with bits 46 from the
bitstream 40 and parses the - in general variable-length - codewords. The read
codewords 44 are inserted into a codeword buffer 43, which represents a first-in-first-out
buffer. A bin decoder 22 sends a request for one or more codewords 41 to the codeword
buffer 43 and as response to this request, the one or more codewords are removed from the
codeword buffer (in sequential order) and send to the corresponding bin decoder 22. Note
that with this embodiment, the potentially complex codeword parsing can be done in a
background process and it doesn't need to wait for the bin decoders. The bin decoders
access already parsed codewords, the potentially complex codeword parsing is no more
part of a request to the overall buffer. Instead already parsed codewords are send to the bin
decoders, which can also be implemented in a way that only codeword indices are send to
the bin decoders.
Interleaving of fixed-length bit sequences
A further way of reducing the PIPE decoder complexity can be achieved when the bin
decoders 22 don't read variable-length codewords from the global bit buffer 38, but instead
they always read fixed-length sequences of bits from the global bit buffer 38 and add these
fixed-length sequences of bits to a local bit buffer, where each bin decoder 22 is connected
with a separate local bit buffer. The variable-length codewords are then read from the local
bit buffer. Hence, the parsing of variable-length codewords can be done in parallel, only
the access of fixed-length sequences of bits has to be done in a synchronized way, but such
an access of fixed-length sequences of bits is usually very fast, so that the overall decoding

complexity can be reduced for some architectures. The fixed number of bins that are sent
to a particular local bit buffer can be different for different local bit buffer and it can also
vary over time, depending on certain parameters as events in the bin decoder, bin buffer, or
bit buffer, However, the number of bits that are read by a particular access does not depend
on the actual bits that are read during the particular access, which is the important
difference to the reading of variable-length codewords. The reading of the fixed-length
sequences of bits is triggered by certain events in the bin buffers, bin decoders, or local bit
buffers. As an example, it is possible to request the reading of a new fixed-length sequence
of bits when the number of bits that are present in a connected bit buffer falls below a
predefined threshold, where different threshold values can be used for different bit buffers.
At the encoder, it has to be insured that the fixed-length sequences of bins are inserted in
the same order into the bitstream, in which they are read from the bitstream at the decoder
side. It is also possible to combine this interleaving of fixed-length sequences with a low-
delay control similar to the ones explained above. In the following, a preferred
embodiment for the interleaving of fixed-length sequences of bits is described.
Fig. 11 shows an illustration of the PIPE encoder structure for the embodiment that
interleaves fixed-length sequences of bits for two or more bin encoders. In contrast to the
embodiment depicted in Fig. 7, the bin encoders 10 are not connected with a single
codeword buffer. Instead, each bin encoder 10 is connected with a separate bit buffer 48,
which stores bits for the corresponding partial bitstream. All bit buffers 48 are connected to
a global bit buffer 51. The global bit buffer 51 is connected to a bit writer 53, which
removes the bits 52 in coding/decoding order from the global bit buffer and writes the
removed bits 54 to the bitstream 55. On a certain events in a particular bit buffer 48 or the
connected bin encoder 10 or bin buffer 8, the bit buffer 48 sends a request 49 to the global
bit buffer 51 by which a certain number of bits is reserved in the global bit buffer 51. The
requests for the reservation of fixed-length bit sequences 49 are processed in sequential
order. The global bit buffer 51 represents a first-in-first-out buffer in a certain way; bits
that are reserved earlier are earlier written to the bitstream. It should be noted that different
bit buffers 48 can reserved a different amount of bits, which can also vary over time based
on already coded symbols; but the number of bits that are reserved by a particular request
is known at the time at which the request is sent to the global bit buffer.
In a particular, the bit buffers 48 and the global bit buffer 51 are operated as described in
the following. The amount of bits that is reserved by a particular bit buffer 48 is denoted as
Nx. This number of bits Nx can be different for different bit buffers 48 and it can also vary
over time. In a preferred embodiment, the number of bits Nx that are reserved by a
particular bit buffer 48 is fixed over time. The reservations for a fixed number Nx of bits 49

are triggered based on the number of bits Mx in the bit buffers 48, the number of bits Nx
for the reservation requests, and the associated maximum codeword length Lx. Note that
each bin encoder 10 can be associated with a different maximum codeword length Lx. If a
bin 7 is sent to a particular bin buffer 8, and the particular bin buffer 8 is empty, and not
more than one sequence of Nx bits is reserved in the global bit buffer for the bit buffer 48
that is connected with the particular bin buffer (via a bin encoder), and the difference
Nx - Mx between the number Nx of bits that are reserved by a reservation request of the bit
buffer 48 that is connected (via a bin encoder) with the particular bin buffer 8 and the
number of bits Mx that are currently present in this bit buffer 48 is less than the maximum
codeword length Lx that is associated with the corresponding bin encoder 10, the
connected bit buffer 49 sends a request 49 for the reservation of Nx bits to the global bit
buffer 51. The global bit buffer 51 reserves Nx bits for the particular bit buffer 48 and
increases its pointer for the next reservation. After the Nx bits have been reserved in the
global bit buffer, the bin 7 is stored in bin buffer 8. If this single bin does already represent
a bin sequence that is associated with a codeword, the bin encoder 10 removes this bin
from the bin buffer 8 and writes the corresponding codeword 47 to the connected bit
buffer 48. Otherwise (this single bin does already represent a bin sequence that is
associated with a codeword), further bins 7 are accepted by the particular bin buffer 8 until
the bin buffer 8 contains a bin sequence that is associated with a codeword. In this case, the
connected bin encoder 10 removes the bin sequence 9 from the bin buffer 8 and writes the
corresponding codeword 47 to the connected bit buffer 48. If the resulting number of bits
Mx in the bit buffer 48 is greater than or equal to the number of reserved bits Nx, the Nx
bits that were first wiitten to the bit buffer 48 are inserted into the previously reserved
space in the global bit buffer 51. For the next bin 7 that is sent to the particular bin
buffer 8, the same process as specified above is executed; i.e., it is checked first whether a
new number of Nx bits must be reserved in the global bit buffer (ifNx - Mx is less than Lx)
and then the bin is inserted into the bin buffer 8, etc. The bit writer writes the fixed-length
bit sequences of the global bit buffer in the order in which they have been reserved. If the
first fixed-length entry in the global bit buffer 51 contains a fixed-length bit sequence that
has been actually inserted in the global bit buffer (i.e., it is not only reserved), the bit
writer 53 removes the bits for this bit sequence 52 from the global bit buffer 51 and writes
the bits 54 to the bitstream. This process is repeated until the first fixed-length entry in the
global bit buffer represents a reserved or a free entry. If the first fixed-length entry in the
global bit buffer represents a reserved entry, the bit writer 53 waits until this entry is filled
with actual bits before it writes further bits 54 to the bitstream 55.

At the end of a data packet, the bin buffers are flushed as described above. In addition, the
bit buffers must be flushed by adding bits with a particular or an arbitrary value until all
reserved buffer entries in the global bit buffer are filled and written to the bitstream.
In Fig. 12, two examples for the possible status of the global bit buffer 51 are illustrated. In
example (a), a case is illustrated in which different bit buffers/ bin encoders reserve a
different number of bits. The global bit buffer contains 3 entries with actually written
fixed-length bit sequences and 4 entries with reserved fixed-length bit sequences. The first
fixed-length entry already contains actual bits (which must have been just inserted by bit
buffer/ bin encoder 2); this entry (i.e., the corresponding 8 bits) can be removed and
written to the bitstream. The next entry reserves 10 bits for bin encoder 3, but actual bits
haven't been inserted yet. This entry cannot be written to the bitstream; it must be waited
until the actual bits are inserted. In the second example (b), all bit buffers/ bin encoders
reserved the same number of bits (8 bits). The global bit buffer contains 4 reservations for
8 bit sequences and 3 actually written 8 bit sequences. The first entry contains a reservation
for 8 bits for bin encoder 3. Before any new bits can be written to the bitstream, the bit
writer has to wait until bit buffer/ bin encoder 3 writes the actual values of the 8 bits into
this reserved entry.
Fig. 13 shows an illustration of the PIPE decoder structure for the embodiment of the
invention that interleaves fixed-length sequences of bits. In contrast to the embodiment
depicted in Fig. 9, the bin decoders 22 are not connected with a single bit buffer. Instead,
each bin decoder 22 is connected with a separate bit buffer 58, which stores bits from the
corresponding partial bitstream. All bit buffers 58 are connected to a global bit buffer 61.
The bits 62 from the bitstream 63 are inserted into the global bit buffer 61. On a certain
events in a particular bit buffer 58 or the connected bin decoder 22 or bin buffer 20, the bit
buffer 58 sends a request 59 to the global bit buffer 61 by which a fixed-length sequence of
bits 60 is removed from the global bit buffer 61 and inserted into the particular bit
buffer 58. The requests for the fixed-length bit sequences 59 are processed in sequential
order. The global bit buffer 61 represents a first-in-first-out buffer; bits that are earlier
inserted into the global bit buffer are earlier removed. It should be noted that different bit
buffers 58 can request a different amount of bits, which can also vary over time based on
already decoded symbols; but the number of bits that are requested by a particular request
is known at the time at which the request is sent to the global bit buffer. It should be noted
that the global bit buffer 61 is not necessarily required, since the codewords could also be
directly read from the bitstream. The global bit buffer 61 is mainly included in the
illustration for clearly separate different aspects of the processing chain.

In an embodiment, the bit buffers 58 and the global bit buffer 61 are operated as described
in the following. The amount of bits that is requested and read by a particular bit buffer 58
is denoted as Nx, it is equal to the amount of bits that is written to the global bit buffer by
the corresponding bit buffer at the encoder side. This number of bits Nx can be different for
different bit buffers 58 and it can also vary over time. In a preferred embodiment of the
invention, the number of bits Nx that are requested and read by a particular bit buffer 58 is
fixed over time. The reading of a fixed number Nx of bits 60 is triggered based on the
number of bits Mx in the bit buffer 58 and the associated maximum codeword length Lx.
Note that each bin decoder 22 can be associated with a different maximum codeword
length Lx. If a request for a bin 19 is sent to a particular bin buffer 20, and the particular
bin buffer 20 is empty, and the number Mx of bits in the bit buffer 58 that is connected (via
a bin decoder) with the particular bin buffer 20 is less than the maximum codeword length
Lx that is associated with the corresponding bin decoder 22, the connected bit buffer 58
sends a request 59 for a new sequences of Nx bits to the global bit buffer 61. As response
to this request, the first Nx bits are removed from to global bit buffer 61 and this sequence
of Nx bits 60 is sent to the bit buffer 58 from which the request was sent. Finally, this
sequence of Nx bits is added to the corresponding bit buffer 58. Then the next codeword 57
is read from this bit buffer, and the connected bin decoder 22 inserts the associated bin
sequence 21 into the connected bin buffer 20. As final response to the original request for a
bin 19, the first bin is removed from the bin buffer 20 and this decoded bin 25 is sent to the
bin buffer selector 18. When the next bin request 19 is sent to the particular bin buffer 20
and the bin buffer is not empty, the next bit is removed from the bin buffer 20. If the bin
buffer is empty but the number Mx of bits in the connected bit buffer 58 is greater than or
equal to the associated maximum codeword length Lx, the next codeword is read from the
bit buffer and a new bin sequence is inserted in the bin buffer, from which the first bit is
removed and sent to the bin buffer selector, If the bin buffer is empty and the number Mx
of bits in the connected bit buffer 58 is less than the associated maximum codeword length
Lx, the next sequence of Nx bits is read from the global bit buffer 61 and inserted into the
connected local bit buffer 58, the next codeword is read from the bit buffer, a new bin
sequence is inserted in the bin buffer, and the first bin of the sequence is removed and sent
to the bin buffer selector. This process is repeated until all source symbols are decoded.
At the end of a data packet, more bins and/or bits than required for decoding the requested
source symbols might be inserted into the bin buffer and/or bit buffer. The remaining bins
in the bin buffer and the remaining bits in the bit buffer are discarded and ignored.
Interleaving of fixed-length bit sequences with a low-delay constraint

The described embodiment for an PIPE encoder and decoder with interleaving of fixed-
length bit sequences can also be combined with the scheme for controlling the encoder
buffer delay, which is described above. The PIPE coding concept is the same as in the
embodiment with delay control described above. If a measure related to the delay or an
upper bound of the delay (see below) exceeds a specified threshold, the first reserved
buffer entry is filled by flushing the corresponding bin buffer (using a similar mechanism
as at the end of a data packet) and potentially writing additional bits for filling all bits of
the reserved fixed-length buffer entry. By such a mechanism, the number of waiting buffer
entries is reduced until the associated delay measure is less than the specified threshold. At
the decoder side, the bins and bits that have been inserted at the encoder side in order to
obey the delay constraint must be discarded. For this discarding of bins and bits basically
the same mechanism as at the encoder side can be used.
In an embodiment, the measure for the delay (or an upper bound of the delay) is the
number of bits in the active buffer entries in the global bit buffer, where the number of
active buffer entries is the number of reserved fixed-length buffer entries plus the number
of fixed-length buffer entries that contain already written bits. Note that the first buffer
entry is always a reserved fixed-length buffer entry or a free buffer entry, since if the first
buffer entry contains written bits, these bits are written to the bitstream. Let the maximum
allowed buffer delay (as determined by the application) be D bits. This maximum buffer
delay D must be known to both encoder and decoder. In a preferred embodiment of the
invention, the maximum buffer delay D is fixed by the application. In another preferred
embodiment of the invention, the maximum buffer delay D is signaled inside the bitstream,
e.g., in the header of the data packet (or slice header) or in a parameter set, which is
included in the bitstream. It can be signaled in units of bits, or bytes, or a multiple of bits,
or a multiple of bytes. If a bin encoder 10 sends a request for the reservation of a new
fixed-length bit sequence to the global bit buffer 51, the following process is executed
before a new fixed-length buffer entry is reserved.
If the number of bits in the active buffer entries in the global bit buffer plus the number of
bits that will be reserved by the current reservation request is greater than the maximum
buffer delay D, the first buffer entry (which is reserved) is flushed by the process described
in the following until the number of bits in the active buffer entries in the global bit buffer
plus the number of bits that will be reserved by the current reservation request is less than
or equal to the maximum buffer delay D. The flushing of a reserved fixed-length buffer
entry is similar to the flushing at the end of a data packet: The bin encoder 10 that is
connected with the bit buffer 48 that has reserved the corresponding first buffer entry is
flushed by adding bins with particular or arbitrary values to the connected bin buffer 8

until the resulting bin sequence represents a bin sequence that is associated with a
codeword, the codeword is then inserted into the corresponding bit buffer 48. As
mentioned above, one preferred way for adding bins to the bin buffer is to add those bins
that produce the shortest possible codeword. If, after the writing of the codeword to the
connected bit buffer and a potential insertion of a fixed-length bit sequence into the global
bit buffer, there are still bits in the bit buffer (i.e., the written codeword did not completely
fill the reserved fixed-length sequence of bits), further bits with particular or arbitrary
values are added to the bit buffer until all bits are removed from the bit buffer and written
to the reserved buffer entry. Finally, at the end of this process, the completed buffer entry
(the first fixed-length entry in the global bit buffer) is removed from the global bit buffer
and written to the bitstream.
At the decoder side, a similar process is executed for discarding the bins and bits that have
been added to obey the delay constraint. Therefore, the decoder maintains a counter C that
counts the bits that have been read from the global bit buffer (this counter can be
maintained in the global bit buffer). The counter C is initialized (e.g. with zero) at the
beginning of the decoding of a data packet and it is increased after a fixed-length sequence
of is read. If a fixed-length sequence of Nx bits is read from the global bit buffer 61, the
counter C is increased by Nx. In addition to the overall counter C, each bit buffer 58
contains a counter Cx, which stores the value of the bit counter C before the last fixed-
length bit sequence was read into the corresponding bit buffer 58. When a particular bit
buffer 58 reads a new fixed-length bit sequence, its counter Cx is set equal to C as a first
step and then the fixed-length bit sequence is read from the global bit buffer 61. When a
request for a bin 19 is sent to a particular bin buffer 20 and the difference (C - Cx)
between the overall counter C and the counter Cx of the connected bit buffer 58 is greater
than the maximum buffer delay D, all bins that are currently stored in the particular bin
buffer 20 and all bits that are stored in the connected bit buffer 58 are discarded and
ignored. Beside that additional step, the decoding is operated as described above. If the bin
buffer 20 to which a request for a bin 19 is sent is empty (either because all bins have
already been removed or because the low-delay mechanism did discard all bins in the first
step after the bin request has been received), the connected bin decoder 22 attempts to read
a new codeword from the connected bit buffer 58. If the number of bits in the bit buffer 58
is less than the maximum codeword length, a new fixed-length bit sequence is read from
the global bit buffer 61, before the codeword is read, etc.
The embodiments just having been described with respect to Figs. 7 to 13 related to
possibilities to achieve an interleaved bitstream path between PIPE encoder 104 on the one
hand and PIPE decoder 202 on the other hand. As has been described above with respect to

Figs. 1 and 2, entropy encoding and decoding apparatus may be connected to each other by
two separate channels, one of which conveys VLC bitstream 112 and the other one of
which conveys the interleaved PIPE encoded bitstream. However, there are also
possibilities to interleave even both the VLC bitstream 112 as well as the PIPE encoded
bitstreams 118, and such possibilities will be described later on with respect to Figs. 20 to
24. However, before that, mathematical background is provided with regard to the PIPE
coding scheme as well as details regarding how to optimally subdivide the probability
interval with assigning the resulting individual partial intervals to the individual entropy
encoders 116 and entropy decoders 210, respectively.
As already noted, in PIPE coding the event space of the input sequence of discrete symbols
is mapped onto a small set of binary probability intervals. The probability models for the
source symbols can be fixed or adaptive while entropy coding using the probability
intervals remains fixed and is decoupled from the modeling stage. Each of the probability
intervals can be coded using a very simple entropy code that has the complexity level of
Huffman codes. The excess rate of the probability interval partitioning entropy (PIPE)
code is similar to that of pure arithmetic coding.
Entropy coding, in general, can be considered as the most generic form of lossless data
compression. Lossless compression aims to represent discrete data with fewer bits than
needed for the original data representation but without any loss of information. Discrete
data can be given in the form of text, graphics, images, video, audio, speech, facsimile,
medical data, meteorological data, financial data, or any other form of digital data. In many
coding applications, the original source data are first mapped onto so-called coding
symbols and these coding symbols are then entropy coded, The mapping onto coding
symbols can include quantization, in which case the overall coding scheme is lossy, A
coding symbol s can take any value of an M -ary (M > 2) alphabet A = {a0,..., aM_^}. For
the purpose of coding the symbol s, the alphabet is associated with an estimated
probability mass function (pmf) {ps(a0),...,ps(aM_])} and all dependencies between
coding symbols that are not considered in this pmf are neglected. For these abstract
settings, the entropy

is the greatest lower bound for the expected codeword length in bits per symbol, for coding
the symbols s, that can be achieved with entropy coding techniques, For decades,
Huffman coding and arithmetic coding have dominated practical entropy coding. They are

well-known examples of practical codes capable of approximating the entropy limit (in a
certain sense).
For a fixed probability distribution, Huffman codes are relatively easy to construct. The
most attractive property of Huffman codes is that their implementation can be efficiently
realized by the use of variable-length code (VLC) tables. However, when dealing with
time-varying source statistics, i.e., changing symbol probabilities, the adaptation of the
Huffman code and its corresponding VLC tables is quite demanding, both in terms of
algorithmic complexity as well as in terms of implementation costs. Also, in the case of
having a dominant alphabet value with /^(a,) > 0.5, the redundancy of the corresponding
Huffman code (without using any alphabet extension such as run length coding) may be
quite substantial. Another shortcoming of Huffman codes is given by the fact that in case
of dealing with higher-order probability modeling, multiple sets of VLC tables may be
required.
Arithmetic coding, on the other hand, while being substantially more complex than VLC,
offers the advantage of a more consistent and adequate handling when coping with
adaptive and higher-order probability modeling as well as with the case of highly skewed
probability distributions. Actually, this characteristic basically results from the fact that
arithmetic coding provides a mechanism, at least conceptually, to map any given value of
probability estimate in a more or less direct way to a portion of the resulting codeword.
Being provided with such an interface, arithmetic coding allows for a clean separation
between the tasks of probability modeling and probability estimation, on the one hand, and
the actual entropy coding, i.e., mapping of symbols to codewords, on the other hand.
Differing from the just-discussed conventional entropy coding schemes, PIPE coding uses
probability interval partitioning, the mathematical background of which is described in
more detail below.
Consider the sequence of coding symbols {s0i...,sN_i}. Each symbol is drawn from an
alphabet s^A,. The alphabets A, = {a!a,a{,...} contain two or more letters each being
associated with a probability estimate ps{a'm). The probability estimates ps(a'm) are
known to encoder and decoder and may be fixed or variable. It is assumed that variable
probabilities are simultaneously estimated at encoder and decoder. The alphabets A, may
either be identical for the sequence of symbols or different symbol types are associated
with different alphabets. In the latter case, it is assumed that the decoder knows the
alphabet of each symbol in the sequence. This assumption is justified as practical source
codec descriptions contain a syntax that stipulates the order of symbols and their alphabets.

The sequence of symbols {s0,..., s^,} is converted into a sequence of binary symbols,
which are also referred to as bins. For each symbol sj, the binarization
b'={%...) = rti*i) (B2)
represents a bijective mapping of the alphabet letters a'm onto ordered sets of bins b 'm . The
binarization mapping y'b can be different for different symbols s, or symbol categories.
Each bin sequence ' for a particular symbol s, consists of one or more bins b\. At the
decoder side, a symbols s. can be reconstructed by the inverse mapping s. = (y'by](b')
given the sequence of bins b '. As a result of the binarization, a sequence of bins
{&„,..., &B_,} is obtained that represents the sequence of source symbols {^0,..., 5W_,}.
All bins bj are associated with the same binary alphabet B = {0,1}, but the corresponding
binary pmfs {pi,pi), with p( = pJ0, are usually different. A binary pmf {pJQ,pf} can be
described by the less probable bin (LPB) value bJLPB and its probability pJLPB (with
pJIPB <0.5). This binary probability description {bJ,PB,pJLPB} can be directly derived
from the probability estimates ps(a'm) for the symbol alphabets given the binarization
mappings y'b. It is also possible (and often preferable) to directly estimate {bJLPB,pJLPB}
simultaneously at encoder and decoder side. Therefore, the bins can be associated with a
probability model (which is also referred to as context) based on the syntax and previously
coded symbols or bins. And for each probability model, the probability description
{bJLPB > PJLPB ) can De estimated based on the values of the bins that are coded with the
probability model. An example for such an binary probability modeling is described with
respect to CABAC of H.264.
Since the binary entropy function
H(p) = -p log2(/7) - (1 - p)log2( 1 - p) (B3)
is symmetric around p=0.5, the same binary coder can be used for coding all bins that are
associated with the same LPB probability pJLPB, independent of the value of bJLPB.
Therefore, the sequence of bins {b0,...,bB_^} is converted into a sequence of coding bins
{60c,...,&£_,}. For each bin b., the corresponding bijective mapping yJc is specified by
baJ=rJAbJ) = bJ®bJLn (B4)

where © denotes the exclusive or operator. At the decoder side, the bins b} can be
reconstructed given the coding bins b° and the corresponding LPB value bJLPB by the
inverse mapping b} = {yJc)"' (b*) = b" © bJLpn . A coding bin bc. = 0 specifies that the value
of corresponding bin b} is equal to the LPB value bJLPB and a coding bin b] ~ 1 specifies
that the value of the corresponding bin b} is equal to the more probable bin (MPB) value
The sequence of coding bins {£>„,..., bcB_{} does uniquely represent the sequence of source
symbols {J0,...,sNA} and the corresponding probability estimates, which can be employed
for entropy coding, are completely described by the LPB probabilities p'lPn (with
pJLPB <0.5). Hence, only probabilities in the half-open interval (0,0.5] need to be
considered for designing the binary entropy coder for the coding bins b?.
For the actual binary entropy coding, the sequence of coding bins {bl,.., ,bcB_x) is projected
onto a small number of probability intervals Jk. The LPB probability interval (0,0.5] is
partitioned into K intervals Ik ~ (pk,pk+l]

The set of K intervals is characterized by K-1 intervals borders pk with k = \,...,K -\.
Without loss of generality we assume pk < pk+] for k-Q,...,K. The outer interval borders
are fixed and given by p0 = 0 and pK - 0.5. A simple non-adaptive binary entropy coder
is designed for each interval Ik. All coding bin bj with associated LPB probabilities
PJLPB 6 h are assigned to the interval Ik and are coded with the corresponding fixed
entropy coder.
In the following description, all bins represent coding bins b* and all probabilities p are
LPB probabilities pJlPB.
For investigating the impact of the probability interval discretization on the coding
efficiency, we assume that we can design an optimal entropy coder for a fixed probability
that achieves the entropy bound. Each probability interval Ik - (pk,pM] is associated with
a representative probability p, elk and the corresponding optimal entropy coder shall

achieve the entropy limit for this representative probability. Under these assumption, the
rate for coding a bin with probability p using the optimal entropy coder for the interval
representative p, is given by

where H(p) represents the binary entropy function 3 and

is its first derivative. We further assume that the distribution of the probabilities in the
(•0.5
interval (0,0.5] is given by f(p), with f(p) dp-\. Then, the expected rate, in bits per
JO
bin, for a given set of K intervals {Ik} with corresponding representative probabilities
{pr } can be written as

The first partial derivative with respect to any representative probability p: , with
k = 0,...,K -l, is given by



for the representative probability p, inside the domain of definition Ik. The second
partial derivative for this solution

is always greater than zero if

Hence, if condition B12 is fulfilled, the value p) given in eq. BIO is the representative
probability for an interval Ik that minimizes the expected overall rate R given the interval
boundaries pk and pk+]. Otherwise, no bin is projected to the interval Ik and the
representative probability pt e Ik can be arbitrarily chosen without any impact on the
overall rate R ; but such a configuration should be avoided, since the interval Ik would not
be employed for entropy coding.
For finding a condition for optimal interval borders, we investigate the first derivatives of
the expected overall rate R with respect to the interval borders pk with k = l,...,K-\. If



for the interval border pk inside the domain of definition [p, ,p, ) and the second
partial derivative for this solution

is always greater than zero, so that p\ is the interval border pk e \p, , p, ) that
minimizes the expected overall rate R given the interval representatives p, and p, . If
there exist probabilities pe[pt ,p, ) with /(/?) = 0, the equation has
multiple solutions, but p* as given in eq. B13 is still optimal even though further optimal
solutions may exist.
Given the number of intervals K and the probability distribution f(p), the interval
borders pk, with k = 1,..., K -1, and the interval representatives p, , with k = 0,..., K -1,
that minimize the expected overall rate R can be obtained by solving the equation system
given by eqs. BIO and B13 subject to the conditions B12 for k = 0,...,K-\. This can be
achieved with the following iterative algorithm.
Algorithm 1:
1) Partition the interval (0,0.5] into K arbitrary intervals Ik = (pk,pk+]] with p0 = 0,
pK = 0.5, and pk < pM for all k - 0,..., K -1 in a way that the conditions B12 are obeyed
for all k = Q,...tK-l.
2) Update the representatives p, with k = Q,...,K-l according to eq. B10
3) Update the interval borders pk with k = l)...,K-\ according to eq. B13
4) Repeat the previous two steps until convergence
Figure 14 shows an example for the optimal interval discretization using the described
algorithm. For this example, we assumed a uniform probability distribution f(p) = 2 for
0 < p < 0.5 and partitioned the probability interval (0,0.5] into K = 4 intervals. It can be
seen that the probability interval discretization leads to a piecewise linear approximation
A(p) of the binary entropy function H(p) with A(p)>H(p) for all pe (0,0.5].

As measure for the impact of the interval discretization on the coding efficiency the
expected overall rate increase relative to the entropy limit

can be used. For the particular example of Figure 14 , the expectation value of the entropy
f(p) dp is equal to 1/(2 In 2) bit per bin and the rate overhead p is equal to
1.01%. Table 4 lists rate overheads p m. and p l!n for the uniform probability distribution
and a linear increasing probability distribution f(p) = Sp with p e (0,0.5], respectively,
for selected numbers of intervals K.
Table 4: Rate overhead vs. the number of probability intervals for the uniform and a linear
increasing probability distribution

The investigations in this section showed that the discretization of the LPB probability
interval (0,0.5] into a small number of intervals with a fixed probability (e.g., 8 to 10
intervals) has a very small impact on the coding efficiency.
The above discussed entropy coding for probability intervals, enables thus of individual
coders using fixed probabilities.
In the following, we first show how an simple code can be designed for fixed probabilities.
Given these results, we develop an algorithms that jointly optimizes the code design and
the partitioning of the LPB probability interval (0,0.5].
The entropy coding for fixed probabilities p- p, can be done using arithmetic coding or
variable length coding. For the latter case, the following approach appears to be simple and
very efficient.

We consider a binary entropy coding scheme by which a variable number of bins is
mapped onto variable length codewords. For unique decodability, the inverse mapping of a
codeword to a bin sequence must be unique. And since we want to design a code that
approaches the entropy limit as close as possible, we constrain our considerations to
bijective mappings. Such a bijective mapping can be represented by a binary tree where all
leaf nodes are associated with codewords, as depicted in Figure 15. The tree edges
represent binary events. In the example of Figure 15, the lower edges represent the LPB
bin value and the upper edges represent the MPB bin value. The binary tree represents a
prefix code for the bins if it is a full binary tree, i.e., if every node is either a leaf or has two
descendants. Each leaf node is associated with a probability based on the given LPB
probability /;, The root node has the probability pro0l =1. The probability for all other
nodes is obtained by multiplying the probability of the corresponding ancestor with p for
the LPB descendants and q = \-p for the MPB descendants. Each leaf node L, is
characterized by the number of LPB edges a, and the number MPB edges b, from the root
node to the leaf node. For a particular LPB probability p, the probability p{ for a leaf
node Ll = {at,b:} is equal to

The binary tree T is fully characterized by the number of leaf nodes L and the associated
pairs {anb,} with / = 0,...,£-l.
Given a full binary tree T and a LPB probability p , the optimal assignment of codewords
to the leaf nodes can be obtained by the Huffman algorithm. The resulting variable number
of bits to variable length codewords (V2V) mapping C is characterized by the number of
codewords L, which is identical to the number of leaf nodes, and the tuples {a,,^,/,} for
l = 0,...,L-l, where /, represents the codeword length that is associated with the
corresponding leaf node L, = {a,, b,}. It should be noted that there are multiple possibilities
for the codeword assignment given the codeword lengths {/,} and the actual codeword
assignment is not important as long as the codewords represent a uniquely decodable
prefix code. The expected rate R(p,C) in bits per bin for a given code C and an LPB
probability p is the ratio of the expected codeword length and the expected number of
bins per codeword


The code design is often limited by factors as the maximum number of codewords L , the
maximum number of bins per codeword, or the maximum codeword length, or it is
restricted to codes of particular structures (e.g., for allowing optimized parsing). If we
assume that the set Sc of usable codes for a particular application is given, the optimum
code C e Sc for a particular LPB probability p can be found by minimizing the expected
rate R(p,C)

As faster alternative, the minimization can also proceed over a given set of binary trees ST
and for each tree only one V2V code C that is obtained by the Huffman algorithm is
considered. As an example, we designed V2V codes for various LPB probabilities p by
considering all binary trees T for which the number of leaf nodes L is less than or equal
to a given maximum Lm. In Figure 16, the relative rate increase
p(p,C\p)) = R(p,C\p))/H(p) is plotted over the LPB probability p for selected
maximum table sizes Lm. The rate increase p(p) can usually be reduced by allowing
larger table sizes. For larger LPB probabilities, a small table size L of 8 to 16 codewords
is usually sufficient for keeping the rate increase p(p) reasonably small, but for smaller
LPB probabilities (e.g., p < 0.1), larger table sizes L are required.
In the previous sections, we considered the optimal probability discretization assuming
optimal codes and the code design for fixed LPB probabilities. But since, in general, we
cannot achieve the entropy limit with real V2V codes of limited table sizes, the code
design and the partitioning of the LPB probability interval (0,0.5] must be jointly
considered for obtaining an optimized entropy coding design.
For a given interval Ik = (pk,pk+l], a code Ck of a given set Sc in an optimal code C*k if it
minimizes the expected rate for the given interval.


For practical designs, the minimization of the integral in eq. B19 can be simplified, with a
minor impact on the coding efficiency, by first determining an optimal representative
probability p] for the interval Ik according to eq. BIO and then choosing the optimal
code C'k of the given set Sc for the representative probability p' according to eq. Bl 8.
Optimal interval borders pk, with k = \,...,K-\, given the set of codes Ck, with
k = 0,,..,K-l, can be derived by minimizing the expected overall rate

Setting the first derivatives with respect to the interval borders equal to zero,
for k = l,..,,K-\, yields

Similarly as for eq. B13, it can be shown that p'k is always an optimal solution, but
depending on the probability distribution f(p) further optimal solutions might exist.
Hence, an optimal interval border p'k between two intervals 7A_, and Ik with given
associated codes Ck_x and Ck, respectively, is the intersection point of the functions
/?(p,Ci.,)andi?(p>CA).
Consequently, the following interactive algorithm can be used for jointly deriving the
probability interval partitioning and the associated codes given the number K of
probability intervals, the set of possible codes Sc, and the probability distribution f(p),
with pe (0,0.5].
Algorithm 2:
1) Derive initial probability interval boundaries pk, with k = 0,..., K, using algorithm
1 specified in sec. 3
2) Derive representatives pr for the probability intervals Ik, with k~Q,...,K-\,
according to eq. BIO

3) Derive codes CkeSc for the interval representatives p, , with k = Q,...,K-l,
according to eq. B18
4) Update the interval borders pk, with k = l,...,K -I, according to eq. B21
5) Repeat the previous three steps until convergence
The steps 2 and 3 in algorithm 2 could also be replaced by a direct derivation of the codes
Ck<=Sc> with k = 0,...,K-l, based on the interval borders pk, with k = 0,...,K,
according to eq. B19. And, as mentioned in sec. 4.1, the minimization in step 3 can also
proceed over a given set of binary trees ST where for each binary tree T only one V2V
code Ck obtained by the Huffman algorithm is considered.
As an example, we jointly derived the partitioning into K = 12 probability intervals and
corresponding V2V codes using algorithm 2. At this, the minimization in step 3 of the
algorithm was replaced with an equivalent minimization over a given set of binary trees
ST where the evaluated code C for each tree T was obtained by the Huffman algorithm.
We considered trees T with a maximum number of Lm - 65 leaf nodes and hence codes
C with up to 65 table entries. All binary trees T with up to 16 leaf nodes have been
evaluated in the minimization; for trees with more than 16 leaf nodes, we employed a
suboptimal search given the best results for trees with a smaller number of leaf nodes.
In Figure 17 the expected rate increase relative to the entropy limit AR(p) = R{p) -H(p)
for the code design example is plotted over the LPB probability p. As comparison, we
also plotted the expected rate increase AR for the theoretically optimal probability interval
discretization (as developed in sec. 3) and the theoretically optimal probability
discretization with the additional constraint p, = 0.5 inside the diagram. It can be seen
that the joint probability interval discretization and V2V code design leads to a shifting of
the interval borders (the interval borders pk, with k- l,...,K-\, are given by the local
maxima of the 6Jl(p) curves). The relative expected overall rate increase relative to the
entropy limit for the design example with real V2V codes is p = 0.24%, when assuming a
uniform probability distribution f(p). The corresponding relative rate increases for the
theoretically optimal probability interval discretization and the theoretically optimal
probability discretization with the additional constraint p, =0.5 are p = 0A2% and
p = 0.13 %, respectively.
Codeword termination can be done as follows. When coding a finite sequence of symbols
{J0,...,5W_,} , each of the K binary encoders processes a finite sequence of coding bins
b ck= {bl,.,., b\ _, }k, with k = 0,...,K~\. And it has been to be ensured that, for each of the

K binary encoders, all coding bins of the sequence b £= {%,...,bB ^}k can be
reconstructed given the codeword or sequence of codewords ck(bck).
Wlien employing arithmetic coding, the arithmetic codeword for the sequence of coding
bins has to be terminated in a way, that all coding bins can be decoded given the codeword.
For the V2V codes described above, the bins at the end of the sequence bck may not
represent a bin sequence that is associated with a codeword. In such a case, any codeword
that contains the remaining bin sequence as prefix can be written. The overhead can be
minimized, if the corresponding codeword that has the minimum length (or one of these
codewords) is chosen. At the decoder side, the additionally read bins at the end of the bin
sequence, which can be identified given the bitstream syntax and binarization schemes, are
discarded.
A simple code design example is presented below. For illustration purposes, we consider
the simple example of a source {s} with three letters and fixed associated probabilities of
ps(a0) = 0.7 , ps(ax) - 0.18 , and ps{a2) = 0.12 . The corresponding ternary choice tree can
be converted into a full binary tree as shown in Fig. 18 .
A binarization for the full binary tree in Fig. 18 is given in Tab. 5 . The ternary symbol
pmf ps is converted into two binary pmfs pb =(0.7,0.3) and p. =(0.6,0.4). For each
symbol s in the bit stream, the bin b0 is present. When ba is equal to 0, also £>, is present.
Note that the binarization given in Tab. 2 is identical to an optimal single-letter Huffman
code for the source 5'.
The entropy for the source s- is
Table 5: Binarization of a three letter source. The LPB probabilities p LPB are 0.3 for the
first bin and 0.4 for the second bin


#(0.7,0.18,0.12) = H (0.7,0.3)4-0.3/7(0.6,0.4)
= 1.1726 bit/symbol (B22)
The average code word length of the single-letter Huffman code is given as

corresponding to a redundancy of pHC = 0.1274 bit/symbol or 10.87% expected rate
overhead.
For the particular binarization example with fixed pmfs, the bins b0 and bx already
represent coding bins, since for both bins the LPB value bJLPn is equal to 0. The
distribution f{s) of the LPB probabilities is discrete, with f(p) - 0 except for p = 0.3
and p = 0.4 . Consequently, the optimal probability discretization leads to K = 2 intervals
with the representatives p, = 0.3 and p, = 0.4. The interval border p] between these
intervals can be arbitrarily chosen in [0.3,0.4) .
For encoding the source, he sequence of source symbols is binarized into a sequence of
bins. The bin ba is transmitted for every source symbol. The bin £, is only transmitted
when bQ = 0. The bins bQ and &, are coded separately with constant LPB probabilities of
Pj = 0.3 and p, = 0.4, respectively.
An efficient coding of a binary alphabet with fixed probability can be achieved by a simple
V2V mapping. Examples for V2V mappings with small coding tables for the LPB
probabilities p LPB = 0.3 and p IPB = 0.4 are given in Tab. 6 and Tab. 7 , respectively.
The V2V mapping for p LPB = 0.3 yields a redundancy of 0.0069 bit/bin or 0.788%. For
the LPB probability of p LPB = 0.4, the redundancy is 0.0053 bit/bin or 0.548%.
Table 6: Bin tree and codes for an LPB probability of p lPD = 0.3. The redundancy of this
code is 0.788%



Table 7: Bin tree and codes for an LPB probability of p Lro = 0.4. The redundancy of this
code is 0.548%

The overall expected rate incurred by the new coding method is

The overall redundancy is 0.73% relative to the entropy limit, which represents a
significant improvement in comparison to the single-letter Huffman code.
It could be argued that a similar coding efficiency improvement could be obtained by
creating a run-length code. For the above example, we could construct a run-length code
for the most probable symbol by considering runs of up to two symbols. Each of the events
{aaaQ,aaa^aQa2,ava2} would be associated with a separate codeword. Such a code yields
a redundancy of 1.34% relative to the entropy limit. Actually, the V2V codes can be
considered as a generalization of run-length codes for binary symbols (the V2V code in
Tab. 3 does effectively represent a run-length code). For a single symbol alphabet with
fixed probabilities, a similar coding efficiency as for the presented approach can also be
achieved by creating a code that maps a variable number of source symbols to variable
length codewords. The main advantage of the presented approach is its flexibility in
mapping arbitrary source symbol sequences with fixed or adaptive probability estimates to
a small number of simple binary coders that are operated with fixed LPB probabilities.
How to achieve an unique decodability is considered next.

With the presented entropy coding scheme, the coding of a sequence of source symbols
s = {s0,...,sN^} consists of the following three basic steps:
• symbol binarization b = {60,...,&/,_1} = yb(s) yielding a sequence of bins
b = {b0,,..,b„_}}
• conversion of the sequence of bins into a sequence of coding bins b c= {bcG,..., bcB^}
= rc(b)
• binary entropy coding of the sequence of coding bins b c= {bc0,..., ¥„_,} using
probability interval discretization and K fixed binary coders
The symbol sequence s = {s0,...,sN^} is uniquely decodable, if the sequence of coding
bins b c= {i>o,... ,6^_,} is uniquely decodable and the mappings yh and yc are invertible.
Let ye notify the encoder mapping of a sequence of one or more coding bins b c= {%,...}
onto a sequence of one or more codewords c(bc)= {co , ...}
c(/;> ye(bc) (B25)
For unique decodability of a sequence of coding bins bc given the sequence of codewords
c(bc), the encoder mapping ye must have the property that a unique codeword c(bc) is
assigned to each possible sequence of coding bins bc:
V^A/ bftbf -> c(b?) * c(bf) (B26)
This property is always fulfilled when arithmetic codes or prefix codes are used. It is
particularly fulfilled for the V2V codes described in sec. 4.1 (including the codeword
termination described in sec. 4.3), since the V2V codes represent prefix codes for variable
numbers of bins.
However, in the presented entropy coding approach, the sequence of coding bins b c is
partitioned into K sub-sequences °k, with k = 0,...,K-l,
{boc,...,bK.f}=yp(bc) (B27)
and to each of the sub-sequences b \, a sequence of codewords Ck(6k°) is assigned using a
particular encoder mapping y\. Consequently, the condition on unique decodability has to
be extended. A sequence of coding bins b c is uniquely decodable given K sequences of

codewords c^b)?), with k = 0,...,K-l,if each sub-sequence of coding bins b\? is uniquely
decodable given the corresponding codeword Ck(6kC) and the partitioning rule y is known
to the decoder. The partitioning rule y is given by the LPB probability interval
discretization {Ik} and the LPB probabilities p'LPB that are associated with the coding bins
bCj, with j = 0,...,B-\. Hence, the LPB probability interval discretization {Ik} has to be
know at the decoder side and the LPB probability p'LPB for each coding bin bc.t with
j = 0,..., B -1, has to derived in the same way at encoder and decoder side.
For the mapping yc of a sequence of bins onto a sequence of coding bins c, each single
b., with j = 0,..., B -1, is converted by the binary mapping bc} - yJc {b. ) = b.® bJLPB , At
the decoder side, the bin sequence can be derived by the binary mappings

with j = 0,..., B -1. If the LPB value b'LPB for each bin b} is derived in the same way at
encoder and decoder side, these mappings (yJc)~] represent the inverses of the
corresponding encoder mappings yJc, since
b) © yLPB = bj © b{PB © yLPB = bj © o=b. (B29)
and hence, the conversion yb of a sequence of bins b into a sequence of coding bins bc is
invertible.
Finally, we investigate the invertibility of the binarization b=yb(s) by which each symbol
sn with i = 0,...,N-l, is mapped onto a bin sequence b '~y'b(s.). A symbol sj can be
uniquely decoded given the corresponding bin sequence b ' if the binarization mapping y'b
assigns a.different bin sequence b Jm to each letter a'm of the alphabet A. for the symbol s,.
However, this condition is not sufficient, since the partitioning of the bin sequence b
= {fe0,...,£>£_,} into bin sequences b' that correspond to the symbols s,, with
/ = 0,..., N -1, is not known to the decoder. A sufficient condition is given, when for each
symbol s,, the bin sequences b Jm that are associated with the letters a'm of the
corresponding alphabet A. form a prefix code and the binarization mappings y\ for each
symbol s., with i = 0,..., N -1, are known at the decoder side.

The conditions of unique decodability for the presented entropy coding approach can be
summarized as follows:
• the binarization mappings y'h represent prefix codes and are known to the decoder (in
symbol coding order)
• the probability models (bJLPB, pJLPB) for all bins b. are derived in the same way at
encoder and decoder side
• the partitioning of the LPB probability interval (0,0.5] into K intervals Ik, with
k = 0,...,K-\ ,\s known to the decoder
• the mapping ykt for each probability interval Ik, with k~0,...,K-l, represents a
uniquely decodable code
In the following, we describe examples for the overall encoder and decoder design in more
detail. We concentrate on coding schemes, in which the probability models {bLPB,p LPB}
for the bins are directly estimated at encoder and decoder side and the K binary coders use
V2V mappings described above. Each source symbol s shall be associated with a symbol
category cs, which determines the type of the symbol including its range of values. The
order of symbols and associated symbol categories shall be given by the syntax, which is
presumed to be known at encoder and decoder side.
The block diagram for an example PIPE encoder and PIPE decoder design is illustrated in
Figure 19. At the encoder side, the symbols 5 with associated symbol categories ct are fed
into the binarizer, which converts each symbol s into a sequence of bins b = ycbs (s).
The used binarization scheme y\s is determined based on the symbol category cs. In
addition, the binarizer associates each bin b of a bin sequence 3 with a probability model
indication cb, which specifies the probability model that is used for coding the bin b . The
probability model indication cb can be derived based on the symbol category cs, the bin
number of the current bin inside the bin sequence s, and/or the values of already coded
bins and symbols.
The probability estimator and assigner maintains multiple probability models, which are
characterized by pairs of values {bLPB,pLPB}. It received bins b and associated
probability model indications cb from the binarizer, and forwards the LPB value b lPB and
the LPB probability p LPB of the indicated probability model to the coding bin deriver and
the probability quantizer, respectively. Thereafter, the corresponding probability model
{b LPB, p LPB} is updated using the value of the received bin b.

The coding bin deriver receives bins b and associated LPB values b lpn from the binarizer
and the probability estimator and assigner, respectively, and sends coding bins bc, which
are derived by bc = b®b LPB, to the probability quantizer. The probability quantizer
forwards each coding bin bc to one of the K binary encoders. It contains information
about the LPB probability interval quantization {Ik}. The LPB probability p LPB , which is
associated with a coding bin bc and received from the probability estimator and assigner, is
compared to the interval borders {pk} and probability interval index k, for which
P I.PB e h' *s derived. Then, the coding bin bc is forwarded to the associated binary
encoder.
Each of the K binary encoders consists of a bin buffer and a bin encoder. The bin buffer
receives coding bins bc from the probability quantizer and stores them in coding order.
The bin encoder implements a particular V2V mapping and compares the bin sequence in
the bin buffer with the bin sequences that are associated with codewords. If the bin
sequence in the bin buffer is equal to one of those bin sequences, the bin encoder removes
the bin sequence {bc} from the bin buffer and writes the associated codeword {{bc}) to
the corresponding codeword stream. At the end of the encoding process for a symbol
sequence, for all binary encoders for which the bin buffers are not empty, a terminating
codeword is written as described in sec. 4.3.
The K resulting codeword streams can be separately transmitted, packetized, or stored, or
they can be interleaved (cp. sec. 6.2) for the purpose of transmission or storage.
At the decoder side, each of the K binary decoders consisting of a bin decoder and a bin
buffer receives one codeword stream. The bin decoder reads codewords {{b°}) from the
codeword stream and inserts the associated bin sequence {b°}, in coding order, into the bin
buffer.
The decoding of the symbol sequence is driven by the underlying syntax. Requests for a
symbol s are sent together with the symbol category cs to the binarizer. The binarizer
converts these symbol requests into request for bins. A request for a bin is associated with
a probability model indication cb, which is derived in the same way as in the encoder, and
sent to the probability estimator and assigner. The probability estimator and assigner is
operated similar to its counterpart at the encoder side. Based on the probability model
indication cb, it identifies a probability model and forwards its LPB value b LPB and LPB
probability p [PB to the bin deriver and the probability quantizer, respectively.

The probability quantizer determines one of the K binary decoders based on the LPB
probability p LPB , in the same way as the binary encoder is determined at the encoder side,
removes the first coding bin bc, in coding order, from the corresponding bin buffer, and
forwards it to the bin deriver. The bin deriver receives coding bins bc and associated LPB
values b LPB from the probability quantizer and probability estimator and assigner,
respectively, and determines the bin values b = bc ® b LPB . As final response to a bin
request sent by the binarizer, the bin deriver send the decoded bin value b to the binarizer
and the probability estimator and assigner.
In the probability estimator and assigner, the value of the decoded bin b is used to update
the probability model {b 1PB,pLPB), which was chosen by the associated value cb, in the
same way as at the encoder side. Finally, the binarizer adds the received bin b to the bin
sequence s which has been already received for a symbol request and compares this bin
sequence J with the bin sequences that are associated with symbol values by the
binarization scheme ycbs. If the bin sequence s matches one of those bin sequences, the
corresponding decoded symbol s is output as final response to the symbol request.
Otherwise, the binarizer sends further bin requests until the symbol s is decoded.
The decoding of a symbol sequence is terminated if no further symbol requests, which are
driven by the syntax, are received. The coding bins bc that may be contained in the bin
buffers at the end of the entropy decoding process (as a result of termination codewords)
are discarded.
After having described certain embodiments for the PIPE encoder and the PIPE decoder in
Figs. 1 and 2 with respect to Figs. 3 to 13 and having provided mathematical background
regarding PIPE coding in general with respect to Figs. 14 to 19, with respect to Figs. 20 to
24, more detailed embodiments for entropy encoding and decoding apparatuses are
described. The following embodiments of Fig. 22 to 24 interleave not only the PIPE
encoded bitstreams among each other, but interleave the VLC bitstream and the PIPE
encoded bitstreams altogether. In comparison thereto, the embodiments for PIPE encoders
and PIPE decoders with interleaving for the PIPE encoded bitstreams, namely the
embodiments of Figs. 7 to 13, merely provided for a separate interleaving of the PIPE
encoded bitstreams. As already mentioned above, even these embodiments may serve as a
basis for achieving a completely interleaved bitstream by use of another
interleaver/deinterleaver pair 134 and 228, respectively (see Figs. 1 and 2), such as, for
example, by using bitstream interleaving as shown in Figs. 5 and 6. However, the

embodiments described next perform the interleaving at once on both the VLC bitstream as
well as the PIPE encoded bitstreams with using, in other words, the one-stage
interleaver/deinterleaver 128 and 230, respectively.
Before describing in detail the embodiments where VLC and PIPE coded symbols are
interleaved inside a bitstream, in order to achieve a more suitable tradeoff between
complexity and coding efficiency, a basic structure thereof without interleaving is
described with respect to Fig. 20 and 21.
The structure of the entropy encoding apparatus of Fig. la is shown in Fig. 20. The entropy
encoding apparatus converts a stream of source symbols la, corresponding to the
combination of VLC encoded and PIPE encoded source symbols of Figs. 1 and 2, namely
106 and 218, respectively, into a set of two or more partial bitstreams 12, 12a, with
bitstream 12a corresponding to bitstreams 112 and 206 of Figs. 1 and 2.
As already noted above, each source symbol la may have associated therewith an
indication that specifies whether the source symbol is coded using standard VLC codes
within VLC encoder 22a, which corresponds to VLC encoder 102 in Fig. 1, or as to
whether the source symbol is to be coded with a PIPE coding concept. As already
described above with respect to Figs. 1 and 2, this indication may not be transmitted
explicitly to the decoding side. Rather, the associated indication may stem from the type or
category of the source symbol itself.
The VLC coded symbols lb are coded with standard VLC codes, which in turn, may
depend on the just-mentioned symbol category or symbol type using a VLC encoder 22a.
The corresponding codewords 11a are written to a distinct partial bitstream 12a. The non-
VLC code symbols 1 are coded using PIPE coding as described above with respect to Figs.
1 and 3, for example, whereupon multiple partial bitstreams 12 are obtained. Some of the
source symbols la may have already been binarized in a way that the binarization consists
of two parts as already mentioned above with respect to Fig. la. One of these parts may be
coded with the PIPE approach and written to the corresponding partial bitstreams 12. The
other part of the bin sequence may be coded with the standard VLC codes and written to
the corresponding partial bitstream 12a.
The basic entropy decoding apparatus fitting to the embodiment of Fig. 20 is shown in Fig.
21.

The decoder performs basically the inverse operations of the encoder of Fig. 20, so that the
previously encoded sequence of source symbols 27, 27a is decoded from a set of two or
more partial bitstreams (24,24a). The decoder includes two different process flows: A flow
for data requests, which replicates the data flow of the encoder, and a data flow, which
represents the inverse of the encoder data flow. In the illustration in Fig. 21 the dashed
arrows represent the data request flow, while the solid arrows represent the data flow. The
building blocks of the decoder basically replicate the building blocks of the encoder, but
implement the inverse operations.
In a preferred embodiment of the invention, each symbol request 13a is associated with an
indication that specifies whether the source symbol is coded using standard VLC codes or
with the PIPE coding concept, As already mentioned above with respect to Fig. 20, this
indication may stem from the parsing rules or the syntax of the syntax elements
represented by the source symbol itself. For example, with respect to Figs. 1 and 2, it has
been described that different syntax element types may be associated with the differing
coding schemes, namely VLC coding or PIPE coding. The same may apply for different
portions of binarizations, or more generally, other symbolizations of the syntax elements.
If a symbol is VLC coded, the request is passed to the VLC decoder 22a and a VCL
codeword 23a is read from a distinct partial bitstream 24a. The corresponding decoding
symbol 27a is output. If a symbol is coded with PIPE, the symbol 27 is decoded from a set
of partial bitstreams 24 as described above with respect to Fig. 4, for example.
In another preferred embodiment of the invention, some of the source symbols are
binarized in a way that the binarization consists of two parts. One of these parts is coded
with the PIPE approach is correspondingly decoded from the associated partial bitstreams
24. And the other part of the bin sequence is coded with standard VLC codes and is
decoded with a VLC decoder 22a that reads the corresponding codewords 23a from a
distinct partial bitstream 24a.
Transmission and multiplexing of the partial bitstreams (VLC coded and PIPE
coded)
The partial bitstreams 12, 12a that are created by the encoder can be transmitted separately,
or they can be multiplexed into a single bitstream, or the codewords of the partial
bitstreams can be interleaved in a single bitstream.

In a preferred embodiment of the invention, each partial bitstream for a quantity of data is
written to one data packet. The quantity of data can be an arbitrary set of source symbols
such as a still picture, a field or frame of a video sequence, a slice of a still picture, a slice
of a field or frame of a video sequence, or a frame of audio samples, etc.
In another preferred embodiment of the invention, two or more of the partial bitstreams 12,
12a for a quantity of data or all partial bitstreams for a quantity of data are multiplexed into
one data packet, The structure of a data packet that contains multiplexed partial bitstreams
may be as illustrated in Fig. 5.
The data packet 300 consists of a header and one partition for the data of each partial
bitstream (for the considered quantity of data). The header 301 of the data packet contains
indications for the partitioning of the (remainder of the) data packet into segments of
bitstream data 302. Beside the indications for the partitioning, the header may contain
additional information. In a preferred embodiment of the invention, the indications for the
partitioning of the data packet are the locations of the beginning of the data segments in
units of bits or bytes or multiples of bits or multiples of bytes. In a preferred embodiment
of the invention, the locations of the beginning of the data segments are coded as absolute
values in the header of the data packet, either relative to the beginning of the data packet or
relative to the end of the header or relative to the beginning of the previous data packet. In
a further preferred embodiment of the invention, the locations of the beginning of the data
segments are differentially coded, i.e., only the difference between the actual beginning of
a data segment and a prediction for the beginning of the data segment is coded. The
prediction can be derived based on already known or transmitted information such as the
overall size of the data packet, the size of the header, the number of data segments in the
data packet, the location of the beginning of preceding data segments. In a preferred
embodiment of the invention, the location of the beginning of the first data packet is not
coded, but inferred based on the size of the data packet header. At the decoder side, the
transmitted partition indications are used for deriving the beginning of the data segments.
The data segments are then used as partial bitstreams 12, 12a and the data contained in the
data segments are fed into the corresponding bin decoders and VLC decoders in sequential
order.
Interleaving of codewords (VLC and PIPE codewords)
For some applications, the above described multiplexing of the partial bitstreams (for a
quantity of source symbols) in one data packet can have the following disadvantages: On
the one hand side, for small data packets, the number of bits for the side information that is

required for signaling the partitioning can become significant relative to the actual data in
the partial bitstreams, which finally reduces the coding efficiency. On the other hand, the
multiplexing may not suitable for applications that require a low delay (e.g. for video
conferencing applications). With the described multiplexing, the encoder cannot start the
transmission of a data packet before the partial bitstreams have been completely created,
since the locations of the beginning of the partitions are not known before. Furthermore, in
general, the decoder has to wait until it receives the beginning of the last data segment
before it can start the decoding of a data packet. For applications as video conferencing
systems, these delays can add-up to an additional overall delay of the system of several
video pictures (in particular for bit rates that are close to the transmission bit rate and for
encoders/decoders that require nearly the time interval between two pictures for
encoding/decoding a picture), which is critical for such applications. In order to overcome
the disadvantages for certain applications, the encoder of a preferred embodiment of the
invention can be configured in a way that the codewords that are generated by the two or
more bin encoders and the VLC encoder are interleaved into a single bitstream, The
bitstream with the interleaved codewords can be directly send to the decoder (when
neglecting a small buffer delay, see below). At the decoder side, the two or more bin
decoders and the VLC decoder read the codewords directly from the bitstream in decoding
order; the decoding can be started with the first received bit. In addition, no side
information is required for signaling the multiplexing (or interleaving) of the partial
bitstreams.
The basic structure of an encoder with codeword interleaving is shown in Fig. 22. The bin
encoders 10 and the VLC encoder 10a don't write the codewords directly to the partial
bitstreams, but are connected with a single codeword buffer 29, from which codewords arc
written to the bitstream 34 in coding order. The bin encoders 10 send requests for one or
more new codeword buffer entries 28 to the codeword buffer 29 and later send the
codewords 30 to the codeword buffer 29, which are stored in the reserved buffer entries.
The VLC encoder 10a directly writes the VLC codewords 30a to the codeword buffer 29.
The (in general variable-length) codewords 31 of the codeword buffer 29 are accessed by a
codeword writer 32, which writes the corresponding bits 33 to the produced bitstream 34.
The codeword buffer 29 operates as a first-in-first-out buffer; codeword entries that are
reserved earlier are earlier written to the bitstream.
In a preferred embodiment of the invention, the codeword buffer is operated as follows. If
a new bin 7 is sent to a particular bin buffer 8 and the number of already stored bins in the
bin buffer is zero and there is currently no codeword reserved in the codeword buffer for
the bin encoder that is connected with the particular bin buffer, the connected bin

encoder 10 sends a request to the codeword buffer, by which one or more codeword entries
are reserved in the codeword buffer 29 for the particular bin encoder 10. The codeword
entries can have a variable number of bits; an upper threshold for the number of bits in a
buffer entry is usually given by the maximum codeword size for the corresponding bin
encoder. The next codeword or the next codewords that are produced by the bin encoder
(for which the codeword entry or codeword entries have been reserved) are stored in the
reserved entry or entries of the codeword buffer. If all reserved buffer entries in the
codeword buffer for a particular bin encoder are filled with codewords and the next bin is
sent to the bin buffer that is connected with the particular bin encoder, one or more new
codewords are reserved in the codeword buffer for the particular bin encoder, etc. The
VLC encoder 10a directly writes the VLC codewords 30a to the next free entry of the
codeword buffer 29, i.e. for the VLC encoder the codeword reservation and the writing of
the codeword is done at once. The codeword buffer 29 represents a first-in-first-out buffer
in a certain way. Buffer entries are reserved in sequential order. Codewords for which the
corresponding buffer entries have been reserved earlier are earlier written to the bitstream.
The codeword writer 32 checks the status of the codeword buffer 29, either continuously or
after a codeword 30 is written to the codeword buffer 29. If the first buffer entry contains a
complete codeword (i.e., the buffer entry is not reserved, but includes a codeword), the
corresponding codeword 31 and the corresponding buffer entry are removed from the
codeword buffer 20 and the bits of the codeword 33 are written to the bitstream. This
process is repeated until the first buffer entry does not contain a codeword (i.e., it is
reserved or free). At the end of the decoding process, i.e., if all source symbols of the
considered quantity of data have been processed, the codeword buffer must be flushed. For
that flushing process, the following is applied for each bin buffer/ bin encoder as first step;
If the bin buffer does contain bins, a bin with a particular or an arbitrary value is added
until the resulting bin sequence represents a bin sequence that is associated with a
codeword (as noted above, one preferred way of adding bins is to add such bin values that
produce the shortest possible codeword - or one of those - that is associated with a bin
sequence that contains the for the original content of the bin buffer as prefix), then the
codeword is written to the next reserved buffer entry for the corresponding bin encoder
(and the corresponding) bin buffer is emptied. If more than one buffer entry has been
reserved for one or more bin encoders, the codeword buffer may still contain reserved
codeword entries. In that case, these codeword entries are filled with arbitrary, but valid
codewords for the corresponding bin encoders. In a preferred embodiment of the invention,
the shortest valid codeword or one of the shortest valid codewords (if there are multiple) is
inserted. The VLC encoder does not require any termination Finally, all remaining
codewords in the codeword buffer are written to the bitstream.

Two examples for the status of the codeword buffer are illustrated in Fig. 23. In
example (a), the codeword buffer contains 4 entries that are filled with a codeword (two of
them are VLC entries) and 3 reserved entries. In addition, the next free buffer entry is
marked. The first entry is filled with a codeword (i.e., the bin encoder 2 just wrote a
codeword to a previously reserved entry). In the next step, this codeword will be removed
from the codeword buffer and written to the bitstream. Then, the first reserved codeword
for bin encoder 3 is the first buffer entry, but this entry cannot be removed from the
codeword buffer, since it is only reserved, but no codeword has been written to this entry.
In the example (b), the codeword buffer contains 4 entries that are filled with a codeword
(one of them is a VLC buffer entry) and 4 reserved entries. The first entry is marked as
reserved and hence the codeword writer cannot write a codeword to the bitstream.
Although 4 codewords are contained in the codeword buffer, the codeword writer has to
wait until a codeword is written to the first reserved buffer entry for bin encoder 3. Note
that the codewords must be written in the order in which they were reserved, in order to be
able to invert the process at the decoder side (see below). And further note that a VLC
buffer entry is always completed, since the reserving and writing of the codeword is done
at once.
The basic structure of a decoder with codeword interleaving is shown in Fig. 24. The bin
decoders 22 and the VLC decoder 2a don't read the codewords directly from separate
partial bitstreams, but are connected to a bit buffer 38, from which the codewords 37, 37a
are read in coding order. It should be noted that the bit buffer 38 is not necessarily
required, since the codewords could also be directly read from the bitstream. The bit
buffer 38 is mainly included in the illustration for clearly separate different aspects of the
processing chain. The bits 39 of the bitstream 40 with interleaved codewords are
sequentially inserted into the bit buffer 38, which represents a first-in-first-out buffer. If a
particular bin decoder 22 receives a request for one or more bin sequences 35, the bin
decoder 22 reads one or more codewords 37 from the bit buffer 38 via requests for bits 36.
The decoder can instantaneously decode the source symbols. Similarly, if the VLC decoder
22a receives a request for a new symbol 19a it reads the corresponding VLC codeword 37a
from the bit buffer 38 and returns the decoded symbol 27a. Note that the encoder (as
described above) must ensure by suitably operating the codeword buffer that the
codewords are written in the same order to the bitstream in which they are requested by the
bin decoders. At the decoder, the entire decoding process is triggered by requests for
source symbols. Parameters as the number of codewords that are reserved at the encoder
side by a particular bin encoder and the number of codewords that are read by the
corresponding bin decoder must be the same.

Interleaving of variable-length codewords with a low-delay constraint
The described codeword interleaving does not require that any partitioning information is
sent as side information. And since the codewords are interleaved in the bitstream, the
delay is in general small. However, it is not guaranteed that a particular delay constraint
(e.g. specified by a maximum number of bits that are stored in the codeword buffer) is
obeyed. Furthermore, the required buffer size for the codeword buffer can theoretically
become very large. When considering the example in Fig. 23(b), it might be possible that
no further bins are send to bin buffer 3 and hence the bin encoder 3 will not send any new
codeword to the codeword buffer until the flushing process at the end of the data packet is
applied. Then all codewords for bin encoders 1 and 2 would have to wait until the end of
the data packet, before they can be written to the bitstream. This drawback can be
circumvented by adding a further mechanism to the encoding process (and also to the
decoding process as described later). The basic concept of that additional mechanism is
that if a measure related to the delay or an upper bound of the delay (see below) exceeds a
specified threshold, the first reserved buffer entry is filled by flushing the corresponding
bin buffer (using a similar mechanism as at the end of a data packet). By such a
mechanism, the number of waiting buffer entries is reduced until the associated delay
measure is less than the specified threshold. At the decoder side, the bins that have been
inserted at the encoder side in order to obey the delay constraint must be discarded. For
this discarding of bins basically the same mechanism as at the encoder side can be used.
After having described in detail possibilities for interleaving the bitstreams of VLC and
PIPE coding, in the following, the description again focuses on the already above
mentioned syntax elements decomposed into source symbols as mentioned with respect to
Fig. lb, lc and 2b. For illustration purposes, the following description assumes that the
thus decomposed syntax elements are absolute transform coefficient level. However, this is
just an example, and other types of syntax elements may handled likewise. In particular,
in the following the coding of absolute levels by partitioning and using different entropy
codes in block-based image and video coders is described.
For example, the pictures of a video sequence are usually decomposed into blocks. The
blocks or the colour components of the blocks are predicted by either motion compensated
prediction or intra prediction. The blocks can have different sizes and can be either
quadratic or rectangular. All samples of a block or a colour component of a block are
predicted using the same set of prediction parameters, such as reference indices
(identifying a reference picture in the already coded set of pictures), motion parameters
(specifying a measure for the movement of a blocks between a reference picture and the

current picture), parameters for specifying the interpolation filter, intra prediction modes,
etc. The motion parameters can be represented by displacement vectors with a horizontal
and vertical component or by higher order motion parameters such as affine motion
parameters consisting of 6 components. It is also possible that more than one set of
prediction parameters (such as reference indices and motion parameters) are associated
with a single block. In that case, for each set of prediction parameters, a single intermediate
prediction signal for the block or the colour component of a block is generated, and the
final prediction signal is built by a weighted sum of the intermediate prediction signals.
The weighting parameters and potentially also a constant offset (which is added to the
weighted sum) can either be fixed for a picture, or a reference picture, or a set of reference
pictures, or they can be included in the set of prediction parameters for the corresponding
block. Similarly, still images are also often decomposed into blocks, and the blocks are
predicted by an intra-prediction method (which can be a spatial intra prediction method or
a simple intra prediction method that predicts the DC component of the block). In a corner
case, the prediction signal can also be zero.
The difference between the original blocks or the colour components of the original blocks
and the corresponding prediction signals, also referred to as the residual signal, is usually
transformed and quantized. A two-dimensional transform is applied to the residual signal
and the resulting transform coefficients are quantized. For this transform coding, the blocks
or the colour components of the blocks, for which a particular set of prediction parameters
has been used, can be further split before applying the transform. The transform blocks can
be equal to or smaller than the blocks that are used for prediction. It is also possible that a
transform block includes more than one of the blocks that are used for prediction. Different
transform blocks in a still image or a picture of a video sequence can have different sizes
and the transform blocks can represent quadratic or rectangular blocks.
All these prediction and residual parameters may form the stream of syntax elements 138
and 226, respectively.
The resulting quantized transform coefficients, also referred to as transform coefficient
levels, may then transmitted using entropy coding by any of the above coding schemes. To
this end, a block of transform coefficients levels may be mapped onto a vector (i.e., an
ordered set) of transform coefficient values using a scan, where different scans can be used
for different blocks. Often a zig-zag scan is used. For blocks that contain only samples of
one field of an interlaced frame (these blocks can be blocks in coded fields or field blocks
in coded frames), it is also common to use a different scan specifically designed for field
blocks. A possible coding scheme for encoding the resulting ordered sequence of transform

coefficients is run-level coding. Usually, a large number of the transform coefficient levels
are zero, and a set of successive transform coefficient levels that are equal to zero can be
efficiently represented by coding the number of successive transform coefficient levels that
are equal to zero (the run) by a respective syntax element. For the remaining (non-zero)
transform coefficients, the actual level is coded in form of respective syntax elements.
There are various alternatives of run-level codes. The run before a non-zero coefficient and
the level of the non-zero transform coefficient can be coded together using a single syntax
element. Often, special syntax elements for the end-of-block, which is sent after the last
non-zero transform coefficient, are incmded. Or it is possible to first encode the number of
non-zero transform coefficient levels, and depending on this number, the levels and runs
are coded.
A somewhat different approach is used in the highly efficient CABAC entropy coding in
H.264/AVC. Here, the coding of transform coefficient levels is split into three steps. In the
first step, a binary syntax element coded_block_flag is transmitted for each transform
block, which signals whether the transform block contains significant transform coefficient
levels (i.e., transform coefficients that are non-zero). If this syntax element indicates that
significant transform coefficient levels are present, a binary-valued significance map is
coded, which specifies which of the transform coefficient levels have non-zero values, And
then, in a reverse scan order, the values of the non-zero transform coefficient levels are
coded. The significance map is coded into the syntax element stream 138 as follows. For
each coefficient in the scan order, a binary syntax element significant_coeff_flag is coded,
which specifies whether the corresponding transform coefficient level is not equal to zero.
If the significant__coeff_flag bin is equal to one, i.e., if a non-zero transform coefficient
level exists at this scanning position, a further binary syntax element
last_significant_coeff_flag is coded. This bin indicates if the current significant transform
coefficient level is the last significant transform coefficient level inside the block or if
further significant transform coefficient levels follow in scanning order. If
last_significant_coeff_flag indicates that no further significant transform coefficients
follow, no further syntax elements are coded for specifying the significance map for the
block. In the next step, the values of the significant transform coefficient levels are coded,
whose locations inside the block are already determined by the significance map. The
values of significant transform coefficient levels are coded in reverse scanning order by
using the following three syntax elements. The binary syntax element
coeff_abs_greater_one indicates if the absolute value of the significant transform
coefficient level is greater than one. If the binary syntax element coeff_abs_greater_one
indicates that the absolute value is greater than one, a further syntax element
coeff_abs_level_minus_two is sent, which specifies the absolute value of the transform

coefficient level minus two. This is the kind of syntax element the processing of which is
performed according to Fig. lb, lc and 2b in the following embodiment. Finally, the binary
syntax element coeff_sign_flag, which specifies the sign of the transform coefficient value,
is coded for each significant transform coefficient level. It should be noted again that the
syntax elements that are related to the significance map are coded in scanning order,
whereas the syntax elements that are related to the actual values of the transform
coefficients levels are coded in reverse scanning order allowing the usage of more suitable
context models. It is also possible that an adaptive scan pattern is used for the significance
map as in the first Test-Model of H.265/HEVC. Another concept is used for coding of the
absolute transform coefficient levels for transform blocks larger than 4x4 in the first Test-
Model of H.265/HEVC. In case of transform blocks larger than 4x4, the larger transform
block is partitioned into 4x4 blocks and the 4x4 blocks are coded in the scan order while
for each 4x4 blocks the reverse scan order is used.
In the CABAC entropy coding in H.264/AVC, all syntax elements for the transform
coefficient levels are coded using a binary probability modelling. The non-binary syntax
element coeff_abs_level_minus_two, for example, is first binarized, i.e., it is mapped onto
a sequence of binary decisions (bins), and these bins are sequentially coded. The binary
syntax elements significant_coeff_flag, last_significant_coeff_flag, coeff_abs__greater_one,
and coeff_sign_flag are directly coded. Each coded bin (including the binary syntax
elements) is associated with a context. A context represents a probability model for a class
of coded bins. A measure related to the probability for one of the two possible bin values is
estimated for each context based on the values of the bins that have been already coded
with the corresponding context. For several bins related to the transform coding, the
context that is used for coding is selected based on already transmitted syntax elements or
based on the position inside a block.
After coding the significance map, the block is processed in reverse scan order. As
mentioned before, another concept is used in the first Test-Model of H.265/HEVC.
Transform blocks larger than 4x4 are partitioned into 4x4 blocks and the resulting 4x4
blocks are processed in scan order, while the coefficients of the 4x4 blocks are coded in
reverse scan order. The following description is valid for all 4x4 blocks in the first Test-
Model of H.265/HEVC and H.264/AVC and also for 8x8 blocks in H.264/AVC and this
description may also apply to the construction of the stream of syntax elements 138 and
226, respectively.
If a scan position is significant, i.e., the coefficient is different from zero, the binary syntax
element coeff_abs_greater_one is transmitted within the stream 138. Initially (within a

block), the second context model of the corresponding context model set is selected for the
coeff_abs_greater_one syntax element. If the coded value of any coeff_abs_greater_one
syntax element inside the block is equal to one (i.e., the absolute coefficient is greater than
2), the context modelling switches back to the first context model of the set and uses this
context model up to the end of the block. Otherwise (all coded values of
coeff_abs_greater__one inside the block are zero and the corresponding absolute coefficient
levels are equal to one), the context model is chosen depending on the number of the
coeff_abs_greater_one syntax elements equal to zero that have already been processed in
the reverse scan of the considered block. The context model selection for the syntax
element coeff_abs_greater_one can be summarized by the following equation, where the
current context model index C/+, is selected based on the previous context model index C,
and the value of the previously coded syntax element coeff_abs_greater_one, which is
represented by bint in the equation. For the first syntax element coeff_abs_greater_one
inside a block, the context model index is set equal to C, = 1.

The second syntax element for coding the absolute transform coefficient levels,
coeff_abs_level_jninus_two is only coded, when the coeff_abs_greater_one syntax
element for the same scan position is equal to one. The non-binary syntax element
coeff_abs_level_minus_two is binarised into a sequence of bins and for the first bin of this
binarisation; a context model index is selected as described in the following. The
remaining bins of the binarisation are coded with fixed contexts. The context for the first
bin of the binarisation is selected as follows. For the first coeff_abs_level_minus_two
syntax element, the first context model of the set of context models for the first bin of the
coeff_abs_level_minus_two syntax element is selected, the corresponding context model
index is set equal to C, = 0. For each further first bin of the coeff_abs_level_minus_two
syntax element, the context modelling switches to the next context model in the set, where
the number of context models in set is limited to 5. The context model selection can be
expressed by the following formula, where the current context model index C,+, is selected
based on the previous context model index C,.

As mentioned before, for the first syntax element coeff_abs_remain_minus_two inside a
block, the context model index is set equal to C( = 0. Note, that different sets of context
models bay be defined for the syntax elements coeff_abs_greater_one and

coeff_abs_remain__minus__two. Also note that for the first Test-Model of H.265/HEVC,
transform blocks larger than 4x4 may be partitioned into 4x4 blocks. The partitioned 4x4
blocks may be processed in scanning order and for each partitioned 4x4 block, a context
set may be derived based on the number of coefficients greater than one in the previous
4x4 block. For the first 4x4 block of a transform block larger than 4x4 and for origin 4x4
transform blocks a separate context set may be used.
That is, when ever in the following description context based coding is used for any of the
source symbols into which coeff_abs_greater_one and coeff_abs_remain_minus_two is
decomposed according to the following embodiments, then this context derivation may be
used by assigner 114 and 212 and VLC en/decoder 102 and 202, for example.
In order to reduce the complexity in terms of number of bins processed by CABAC or
PIPE compared to the start-of-the-art techniques and also in terms of computation
complexity or also to increase the coding efficiency, the below outlined embodiment
describes an approach for coding absolute levels by using different variable length codes
for different partitions 140j to HO3 in image and video encoders and decoders. The
embodiments outlined below can be, however, applied to all kind of absolute levels for
image and video coders, like motion vector differences or coefficients of the adaptive loop
filter. While the coding of transform coefficients levels is performed as outlined below the
coding of the significance map may remain as in the first Test-Model of H.265/HEVC or
as has been described above, or the coding of the significance map can also be done as in
H.264/AVC or otherwise.
As described above, the coding of the absolute transform levels is performed in multiple
partitions HO1.3. The coding scheme has exemplary been illustrated in Figure lb with three
partitions I4O1.3. The bounds 142 and 144 of the scheme are variable resulting in variable
partition sizes. The coding scheme is done as follows.
A first entropy code is used to code the first component or source symbol, i.e. absolute
transform coefficient level (z) in case same is smaller than limit 1, or limitl in case same is
not. If the absolute transform coefficient level is greater than or equal to the bound limitl
of the first partition 140i, than the bound limitl (142) of the first partition (1400 is
subtracted from the absolute transform coefficient level and the resulting value z' is coded
with a second entropy code. If the remaining absolute transform coefficient level z' is
greater than or equal to a bound Hmit2-limitl for the second partition 1402, than the bound
limit2-limitl of the second partition is again subtracted from the absolute transform
coefficient level z' and the resulting value is coded with a third entropy code. Generally

speaking, when the bound of a partition is reached, the entropy code for the next partition
to the bound is used to code the value resulting from absolute transform coefficient levels
minus the bound of the corresponding partition.
The entropy codes can be simple variable length codes as run-length codes or lookup tables
(e.g. Huffman code) or more complex entropy codes employing probability models like
CABAC or PIPE. The number of partitions and the bound of the partitions may be variable
or depending on the actual syntax element. The partitioning concept shown in Fig. lb has
the following benefits. In the following, we use the absolute transform coefficients as an
example, but it should be understood the they can be replaced with any other syntax
element. As an example, the probability distribution of the absolute transform coefficient
levels may be approximately a geometric distribution. Therefore, entropy codes optimized
for geometric distributions may be employed for coding the absolute transform coefficient
levels. But such a model is not always locally optimal, even if context modeling and
probability model selection is employed. For example, for a transform block, the local
absolute transform coefficient levels follow a distribution which is not geometrical at all if
it contains the same amount of very low and middle range transform coefficient levels,
while the model may hold true (with a certain accuracy) for a specific amount of blocks in
image or video due to the law of large numbers. For such a case, the geometrical
distribution is not a suitable model. Also, when considering absolute transform coefficient
levels with large values, the distribution of these large values are often uniform. The
partitioning concept allows different probability models for different absolute transform
coefficient levels. For lower absolute values, more complex entropy codes can be applied
for higher efficiency, while for large absolute levels less complex entropy codes can be
employed for reducing the complexity.
As mentioned before, entropy codes suitable for the different partitions are used. In a
preferred embodiment of the invention, three types of entropy codes are employed. The
first entropy code uses PIPE. However, it should be noted that, according to an alternative,
an entropy coding method like CABAC or any other arithmetic coder may be used
alternatively. That is, the first symbols Si (see Fig. 2b) may be coded via the PIPE coding
path. Subdivider 100 and recombiner 220 act accordingly.
For the second type, Golomb codes and some truncated variants including subsets (e.g.
Golomb-Rice codes) may be used. That is, the second symbols S2 (see Fig. 2b) may be
coded via such VLC codes in VLC en/decoder 102/202. Subdivider 100 and recombiner
220 act accordingly.

Exponential-Golomb codes are used as the third type. That is, the third symbols S3 (see Fig.
2b) may be coded via such VLC codes in VLC en/decoder 102/202. Subdivider 100 and
recombiner 220 act accordingly. Different VLC codes and different combinations of VLC
and PIPE or VLC and arithmetic codes are possible.
While the first code is more complex but yields better compression performance, the
second entropy codes represent a reasonable trade-off between complexity and
performance. The last entropy codes, e.g. Exponential-Golomb codes, are very low
complex. In the following, the coding of the different partitions is described.
If a partition such as partition 140i, such as the symbol si, is to be entropy coded using an
entropy coder employing probability models like PIPE coder 104 (again, CAB AC or any
other arithmetic coder may be used in an alternative not described further here), subdivider
120 directs same towards PIPE encoder 104. Firstly, the non-binary valued absolute
transform coefficient levels may be binarised in symbolizer 122 using a binarisation
method. The binarisation maps the non-binary valued absolute transform coefficient levels
to a sequence of binary bins. Each bin of the bin string is coded with a context chosen by
assigner 114. The context modeling can be done for the first bin and fixed for the
following bins of the bin sequence as coeff_abs_level_minus_two in H.264/AVC or a
different context modeling may be used for each bin of the bin string. Note that the
binarisation can be a variable-length code like Golomb codes or Exponential-Golomb
codes or other variable-length codes.
Next, a partition such as partition 1402 or symbols S2 may be coded with a Golomb code,
here in VLC encoder 102 and respectively decoded in VLC decoder. Golomb codes are a
set of entropy codes designed for geometrical distributed source. If the order of the
Golomb code is zero, the Golomb code is also known as unary code. The unary code is
related to the binarisation of coeff_abs_level_minus_two in H.264/AVC. Golomb codes
are constructed as follows. For a specific Golomb parameter k, the value n is divided by
the Golomb parameter k using integer division and the remainder r is calculated.

After deriving the parameters specified by the formulas above, the value n can be coded
with two parts. The first part, also referred as prefix part, is a unary code. The resulting

value p +1 specifies the number of ones and a terminating zero or vice versa. The
remainder value, also referred as remainder part and denoted by r, is represented with a
truncated binary code. In accordance with a specific embodiment, the Golomb-Rice codes
are employed for coding the source symbols such as source symbols S2 the Golomb-Rice
codes being a subset of Golomb codes. Also, when using such entropy codes for partitions
140]_3 containing a bound, such as partition 1402 the alphabet of the respective source
symbols (such as source symbols S2) is limited and the Golomb-Rice code can be modified
so that the coding efficiency can be improved. The parameter of the Golomb-Rice code can
be fixed or variable. If the parameter is variable, the parameter may be estimated as a part
of context modelling stage. For example, if a source symbol S2 enters VLC encoder 102,
the latter may determine the parameter of the Golomb-Rice code from a context of S2. The
Golomb-Rice codes are Golomb codes with parameters to the power of two. So they are
based on division and multiplication by two and therefore they can be implemented
efficiently in a binary architecture with shift and addition operations. The relation between
the Golomb-Rice parameter and the Golomb parameter is therefore kGOLOm = 2 Ria'. In
case of Golomb-Rice code, the remainder part is exactly the binary representation of the
remainder value. For the Golomb-Rice parameter of zero, the resulting code is identical to
the unary code and does not have a remainder part. For the parameter equal to one, the
remainder part consists of one bin with two input symbols sharing the same unary prefix.
In the following, some example tables for selected Golomb-Rice parameters are illustrated.

Given the range of the partition such as for example limit2-limitl in case of partition MO2
and the parameter of the Golomb-Rice code, the truncation can be done as follows. The
Golomb-Rice parameter describes the number of bins required to represent the remainder
part and the two to the power of the parameter value describes the number of values, which

can be represented with the same prefix. These values form a prefix group. For example,
for the parameter zero, only one prefix can represent one specific value, while for the
parameter three, eight input values share the same prefix and therefore a prefix group
contains eight values for the parameter three. For a limited source alphabet and a given
Golomb-Rice code, the last bin of the prefix can be left out for values in the last prefix
group resulting in a prefix code with fixed length.
For example, the range may be nine and the Golomb-Rice parameter is two. For this
example case, the number of values which can be represented with a same prefix is four.
The maximum value is nine, which also indicates that the border is exceeded and the next
entropy code of the next partition has to be used. In this example case, the values from 0 -
3 have the prefix 0, the values from 4-7 have the prefix 10 and 8-9 the prefix 110.
Because the values 8-9 formed the last prefix group, their trailing zero can leave out and
the values 8-9 can be represented by 11. In other words, imagine, a source symbol S2
entered VLC encoder 102 with the number of possible values of S2 being 9 (=limit2-
limitl+1) and the Golomb-Rice parameter for that source symbol being two. Then, a
respective Golomb-Rice codeword would be output by VLC encoder 102 for that source
symbol, which has a prefix as just described. For the remainder part of the codeword, the
truncated code may be derived as follows by VLC encoder 102. Normally, the parameter
of the Golomb-Rice codes indicates the number of bins of the remainder part. In a
truncated case, not all bins of the remainder need to be coded. For a truncated case, all
values with fixed prefix (e.g. a bin of the prefix is left out) are counted. Note that the
counted value is always smaller than or equal to the maximum number of values for a
prefix because the code is truncated. If a truncation of the remainder part is possible, the
derivation of the truncated remainder part for the last prefix group can proceed in the
following steps. First, the largest number /to the power of two smaller or equal than the
counted number is derived. Then, in the second step, the smallest number h to the power of
two greater than the counted number is derived. The first value / describes the number of
values in the prefix group with a remainder of h bins. All remainders of these values
begins with a 0 followed by the binary representation of the remainder limited to the
number of values in the remainder group. For the remaining values of the last prefix group,
now treated as a new prefix group, the same procedure is done except for the resulting
values formed the first remainder group, the remainder begins with a 1. This procedure is
done until all remainders are derived. As an example, the range is 14 and the parameter is
three. The first prefix group contains values from 0-7 and the second prefix group values
from 8-13. The second prefix group contains six values. The parameters are 1 = 2 and
h = 3. So, the first four values of the prefix groups are represented by a remainder with
three bins (a trailing zero and the binary representation to distinguish the four values). For

the last two values, the same procedure is done again. The parameters are l = \ and h = 2.
The remainder of the last two values now can be represented as 10 and 11. Another
example to demonstrate the method is a Golomb-Rice parameter of four and a range often.
For this example, the parameters are 1 = 3 and h = 4. With these parameters, the truncated
remainder part for the first eight values are represents by four bins. The remaining two
values have the same remainder part as in the previous example before. If the range is nine
for the previous example, the parameter for the second run is / = 0 and h = 1. The
remainder part of the only one value that remains is 1.
The third type of entropy codes may be Exponential-Golomb codes. They may be
employed for equal probable distributions (e.g. with parameter zero) such as source
symbols S3. That is, the VLC encoder/decoder pair may responsible for their coding. As
mentioned before, larger absolute transform coefficient levels are often uniformly
distributed. More precisely, the zero-order Exponential-Golomb code may be used to code
the last partition 1403. The beginning and therefore the border 144 to the previous partition
1402 may be variable. The position of border 144 may be controlled by VLC en/decoder
102/200 in dependency of preciously encoded/decoded source symbols 106, 108 and/or
110 or syntax elements 138 (or 218, 204 and/or 208 or syntax elements 226).
In a preferred embodiment, the number of partitions is three as shown in Fig. lb and the
bounds 142 and 144 may be variable. For the first partition 140], PIPE coding may be
employed as discussed above. However, alternatively CAB AC may be used as well. In that
case, PIPE en/decoder pair would be replaced by a binary arithmetic coding en/decoder
pair. The truncated Golomb-Rice codes may be used for the second partition 1402 and the
zero-order Exponential-Golomb code may be used for the last partition 1403.
In another preferred embodiment, the number of partitions HO1.3 is three and the first
bound 142 is fixed, while the second bound 144 is variable. For the first partition 140j,
CABAC or PIPE is employed. The truncated Golomb-Rice codes may be used for the
second partition 1402 and the zero-order Exponential-Golomb code may be used for the
last partition I4O3.
In another preferred embodiment, the number of partitions is equal to two. The first
partition 140i could use CABAC or PIPE. The second partition could use Golomb-Rice
codes such as HO2.
In another preferred embodiment, the number of partitions is equal to three while both
borders 142 and 144 are variable. For instance, for the first partition 140i, CABAC or PIPE

is employed, while the second partition 1402 may use the truncated Golomb-Rice code and
the third partition 1403 uses zero-order Exponential-Golomb code.
In a preferred embodiment, the bound 142 of the first partition 140i using CAB AC or
PIPE, which employs adaptive probability models, is two. In this preferred embodiment,
the context modeling for the first bin may be done as described for coeff_abs_greater_one
as described above and the context modeling for the second bin may be done as described
for coeff_abs_level_minus_two in H.264/AVC as has also been described above. The latter
context determination would be determined by assigners 114 and 212, respectively. In
another preferred embodiment, the bound 142 of the first partition 140j using entropy
coding that employs probability modeling (e.g. PIPE or CABAC) is two. For this preferred
embodiment, the context modeling for both the first and the second bin may be done as
described for coeff_abs_greater_one in H.264/AVC as described above. The context set
evaluation as described for coeff_abs_greater_one may be done separately for the second
bin.
In a preferred embodiment, the bound 142 of the first partition 140i using entropy coding
employing probability modeling (e.g. CABAC or PIPE) may be equal to one. For the only
bin (or alphabet symbol) of the bin string of the respective source symbol, the context
modeling may be done as described for coeff_abs_greater_one in H.264/AVC previously
described.
In a preferred embodiment, the bound 142 of the first partition 140i using entropy coding
employing probability modeling (e.g. CABAC or PIPE) may be three. The context
modeling of the first and second bins of the bin string of the respective source symbol may
be done as coeff_abs_greater_one in H.264/AVC. The context modeling for the third bin
may be done as coeff_abs_level_minus_two in H.264/AVC. The context set evaluation as
described for coeff_abs_greater_one may be done separately for the second bin.
In a preferred embodiment, a set of truncated Golomb-Rice codes may be used as entropy
codes of the second partition 1402. The bound 144 of the second partition specifying the
beginning of the third partition I4O3 depending on the entropy code parameter may be
variable. Also in this preferred embodiment, the Golomb-Rice parameter may be limited
by three and the parameter selection maybe done as the context modeling for
coeff_abs_level_minus_two in H.264/AVC. The range limit-limit2 may be variable and
may depend on the Golomb-Rice parameter. If the parameter is zero, the range is 8. For the
parameter one, the range is 10. In case of parameter two, the range is 12 and for the
parameter three, the range is equal to 16. In this preferred embodiment, the Golomb-Rice

parameter is set to zero at the beginning of a block of transform coefficients. For each
coded transform coefficient level in the block larger or equal than the first bound, the
corresponding Golomb-Rice code used. After coding (or decoding) a level, the following
evaluation is made to update the Golomb-Rice parameter for coding (or decoding) of the
next level greater or equal than the first bound. Note that the Golomb-Rice parameter
cannot be decreased by using this form of adaptation.
The parameter adaptation rule can be summarized as follows, where kl+] denotes the
Golomb-Rice parameter to be used for coding of the next level value and value, denotes
the previously coded value with corresponding Golomb-Rice parameter k,

In a preferred embodiment, a set of truncated Golomb-Rice codes may be used as entropy
codes of the second partition 14C>2. The bound 144 of the second partition MO2 specifying
the beginning of the third partition HO3 depending on the entropy code parameter may be
variable. Also in this preferred embodiment, the Golomb-Rice parameter may be limited
by three and the parameter selection may be done as context modeling for
coeff_abs_level_minus_two in H.264/AVC. The range may be variable and depend on the
Golomb-Rice parameter. If the parameter is zero, the range is 8. For the parameter one, the
range is 10. In case of parameter two, the range is 12 and for the parameter three, the range
is equal to 16. In this preferred embodiment, the Golomb-Rice parameter is set to zero at
the beginning of the block. The Golomb-Rice parameter adaptation is performed as
described by equation (QQ). Note that the parameter cannot be decreased by using this
form of adaptation.
In another preferred embodiment, a set of truncated Golomb-Rice codes may be used as
entropy codes of the second partition 1402. The bound 144 of the second partition 1402
specifying the beginning of the third partition HO3 depending on the entropy code
parameter may be fixed. Also in this preferred embodiment, the Golomb-Rice parameter
may be limited to three and the parameter selection may be done as context modeling for
coeff_abs_level_minus_two in H.264/AVC. The range of the second partition HO2 may be
fixed to 14. In this preferred embodiment, the Golomb-Rice parameter may be set to zero
at the beginning of the block. The Golomb-Rice parameter adaptation is performed as

described by equation (QQ). Note that the parameter cannot be decreased by using this
form of adaptation.
In another preferred embodiment, a set of truncated Golomb-Rice codes may be used as
entropy codes of the second partition 1402. The bound 144 of the second partition 1402
specifying the beginning of the third partition 1403 depending on the entropy code
parameter may be variable. Also in this preferred embodiment, the Golomb-Rice parameter
may be limited to three and the parameter selection may be done as context modeling for
coeff_abs_level_minus__two in H.264/AVC. The range may be variable and depend on the
Golomb-Rice parameter. If the parameter may be zero, the range may be 8. For the
parameter one, the range may be 10. In case of parameter two, the range may be 12 and for
the parameter three, the range may be equal to 16. In this preferred embodiment, the
Golomb-Rice parameter may be set to zero for at the beginning of the block. The Golomb-
Rice parameter adaptation is performed as described by equation (QQ). Note that the
parameter cannot be decreased by using this form of adaptation. And also note that a direct
switching, e.g. from zero to three, is possible. In this preferred embodiment, the prefix part
of the Golomb-Rice codes is coded with entropy codes employing probability models. The
context modeling can be done as for coeff__abs_level_minus_two in H.264/AVC.
In another preferred embodiment, a fixed Golomb-Rice parameter may be used to code all
transform coefficient levels in current transform block. In this embodiment, the best
parameter of the previous block may be calculated and used for the current transform
block. For this embodiment, the range may be fixed by 14.
In another preferred embodiment, a fixed Golomb-Rice parameter may be used to code all
transform coefficient levels in current transform block. In this embodiment, the best
parameter of the previous block may be calculated and used for the current transform
block. For this embodiment, the range may be variable as described before.
In another preferred embodiment, it is evaluated if the already coded (or decoded)
neighborhood of the current scan index contains absolute transform coefficient levels
larger than the previous bound. For this preferred embodiment, the best parameter may be
derived by using neighbors in a local causal template.
Thus, above-mentioned embodiments inter alias described, an entropy encoding apparatus
comprising a decomposer 136 configured to convert a sequence 138 of syntax elements
into a sequence 106 of source symbols 106 by individually decomposing at least a
subgroup of the syntax elements into a respective number n of source symbols s-{ with

i=l.. .n, the respective number n of source symbols depending on as to which of a sequence
of n partitions 140[_3 into which a value range of the respective syntax elements is sub-
divided, a value z of the respective syntax elements falls into, so that a sum of values of the
respective number of source symbols s; yields z, and, if n>l, for all i=l ...n-1, the value of
Si corresponds to a range of the ith partition; a subdivider 100 configured to subdivide the
sequence 106 of source symbols into a first subsequence 108 of source symbols and a
second subsequence 110 of source symbols such that all source symbols sx with x being
member of a first subset of {l...n} are contained within the first subsequence 108 and all
source symbols sy with y being member of a second subset of {1.. .n} being disjoint to the
first subset, are contained within the second subsequence 110; a VLC encoder 102
configured to symbol-wisely encode the source symbols of the first subsequence 108; and
a PIPE or arithmetic encoder 104 configured to encode the second subsequence 110 of
source symbols.
The values z of the subgroup of the syntax elements may be absolute values. The second
subset may be {1} with the sequence of n partitions being arranged such that a pth partition
covers higher values of the value range than a qth partition for all p,q e {l..n} with p>q. n
may be 3. The first subset may be {2,3} with the a VLC encoder (102) configured to use a
Golomb-Rice code to symbol-wisely encode the source symbols S2, and a Exp-Golomb
Code to symbol-wisely encode the source symbols S3. More generally, 2 may be element of
the first subset with the a VLC encoder (102) being configured to use a Golomb-Rice code
to symbol-wisely encode the source symbols s2 and adapt a Golomb-Rice parameter, i.e. k,
of the Golomb-Rice code according to previously encoded source symbols. The
decomposer may be configured to adapt one or more of the limits between the partitions
according to previously encoded source symbols. Both adaptations may be combined. That
is, positions of the limits limiting the second partition may be adapted such that they are
spaced apart from each other such that the length of the Golomb-Rice code, i.e. the number
of codewords thereof, corresponds to (or prescribes) the length of the width of the second
partition. The limit between separating the first from the second partition may be defined
otherwise such as being fixed by definition or adapted in accordance with other context
dependency, in what case the adaptation of k may define the position of the limit
separating the second and third partition via the length of the Golomb-Rice code and the
width of the second partition, respectively. By coupling the adaptation of k so that the
width of the second partition corresponds to the length of the Golomb-Rice code, the code
efficiency is optimally used. Adapting k to the statistics of the syntax element enables to
adapt the width of the second partition such that the third partition may cover as much as
possible so as to reduce the overall coding complexity since a lower complex code may
have be used for the third partition such as the Exp-Golomb code, Further, the length of the

first partition may be restricted to j e {1, 2, 3} possible syntax element values, such as the
lowest three levels. The syntax elements under consideration may be differentially coded
or represent a prediction residual such is the case with the above exemplified transform
coefficient levels which represent a prediction residual. The first source symbols si may be
symbolized/desymbolized by use of a truncated unary code with the resulting j bins being -
partially or all-of them - coded context-adaptively or not as mentioned above.
The subgroup of the syntax elements may encompass absolute transform coefficient levels
of absolute transform coefficients of transform blocks of a picture with the absolute
transform coefficient levels of a respective transform block being arranged within the
sequence (138) of syntax elements in accordance with a scan path leading through the
absolute transform coefficients of the respective transform blocks, wherein the decomposer
may be configured to adapt one or more of limits between the partitions during
decomposing the absolute transform coefficient levels of the absolute transform
coefficients of a respective transform block depending on already encoded absolute
transform coefficient levels of absolute transform coefficients of the respective transform
blocks preceding in the scan order or depending on a position of the absolute transform
coefficient level currently to be decomposed in the scan order, or based on an evaluation of
the already reconstructed absolute transform coefficient levels of transform coefficients
neighboring - either spatially or in scan order - the position of the absolute transform
coefficient level currently to be decomposed.
Further, the above-mentioned embodiments inter alias describe an entropy decoding
apparatus comprising a VLC decoder 200 configured to codeword-wisely reconstruct
source symbols of a first subsequence 204 of source symbols from codewords of a first
bitstream 206; a PIPE or arithmetic decoder 202 configured to reconstruct a second
subsequence 208 of source symbols; a composer 224 configured to compose a sequence
226 of syntax elements from the first subsequence 204 of source symbols and the second
subsequence 208 of source symbols by individually composing each syntax element from a
respective number of source symbols, wherein the composer is configured to, for at least a
subgroup of the syntax elements, determine the respective number n of source symbols Sj
with i=l...n depending on as to which of a sequence of n partitions 140i_3 into which a
value range of the respective syntax elements is sub-divided, a value z of the respective
syntax elements falls into, by summing-up the values of the respective number of source
symbols s,- from 1 to n as long as the value of s; corresponds to a range of the ith partition so
as to obtain the value of the syntax element z, wherein the composer 224 is configured to
retrieve all source symbols sx with x being member of a first subset of {l...n} from the
first subsequence (204) and all source symbols sy with y being member of a second subset

of {1.. .n} being disjoint to the first subset, from the second subsequence 208. The values z
of the subgroup of the syntax elements may be absolute values. The second subset may be
{1} with the sequence of n partitions being arranged such that a pth partition covers higher
values of the value range than a qth partition for all p,q e {l..n} with p>q. n may be 3. The
first subset may be {2,3} with the a VLC decoder 200 being configured to use a Golomb-
Rice code to codeword-wisely reconstruct the source symbols S2, and a Exp-Golomb Code
to codeword-wisely reconstruct the source symbols S3. More generally, 2 may be element
of the first subset with the a VLC decoder 102 being configured to use a Golomb-Rice
code to codeword-wisely reconstruct the source symbols S2 and adapt a Golomb-Rice
parameter of the Golomb-Rice code according to previously reconstructed source symbols.
The entropy decoding apparatus may further comprise a recombiner 220 configured to
recombine the first subsequence 204 of source symbols and the second subsequence of
source symbols to obtain the sequence 218 of source symbols. The syntax elements may be
of different type and the composer may be configured to perform the individual composing
depending on the type of the syntax elements. The subgroup of the syntax elements may
encompass absolute transform coefficient levels of absolute transform coefficients of
transform blocks of a picture with the absolute transform coefficient levels of a respective
transform block being arranged within the sequence 138 of syntax elements in accordance
with a scan path leading through the absolute transform coefficients of the respective
transform blocks, wherein the composer may be configured to adapt one or more of limits
between the partitions during composing the absolute transform coefficient levels of the
absolute transform coefficients of a respective transform block depending on already
reconstructed absolute transform coefficient levels of absolute transform coefficients of
the respective transform blocks preceding in the scan order or depending on a position of
the absolute transform coefficient level currently to be composed in the scan order, or
based on an evaluation of the already reconstructed absolute transform coefficient levels
of transform coefficients neighboring - either spatially or in scan order - the position of the
absolute transform coefficient level currently to be composed.
Regarding the embodiments combining PIPE coding with VLC coding using the
decomposition according to Fig. lb, the following is noted in order to repeat some aspects
thereof in other words.
The mapping of a sequence of symbols to a bit stream and the inverse mapping has been
described. Each symbol carries associated parameter(s) with it that are simultaneously
known at encoder and decoder. The entropy codec contains multiple first-in first-out
(FIFO) buffers with each of them assigned to subsets of parameter(s) that are associated to
the symbols. For given parameter(s) of a symbol, the encoder assigns the symbol to the

corresponding FIFO buffer. Since the encoder assignment rule is known at the decoder
side, the decoder reads from the FIFO buffer to which the encoder has assigned the
symbol.
Some syntax elements are coded using standard variable-length codes and are written to a
particular buffer. Other syntax elements are coded using the probability interval
partitioning entropy (PIPE) coding concept. At this, the symbols are first binarized and the
resulting bins are classified based on associated probability estimates. The probability
estimate may be given or derived from a measurement that can be conducted
simultaneously at encoder and decoder. A particular FIFO buffer contains symbols with
estimated probability values falling into a subset of probabilities that is chosen, so that the
entropy coding can be improved. The improvement achieved by a combination of the PIPE
concept with VLC is a complexity reduction while still providing a high coding efficiency.
Symbols for which a standard VLC code is suitable are coded with the simple and low-
complex VLC approach, while other symbols for which the bit rate would be significantly
increased by coding them with a VLC code are coded with the more sophisticated PIPE
concept.
Thus, in order to further reduce the complexity of entropy coding, the symbols have been
split into two categories. Symbols of a first category can well be represented with VLC
codes and don't require the more complex PIPE coding, while symbols of a second
category cannot be efficiently represented with VLC codes and a PIPE coding for these
symbols significantly reduced the required bit rate.
It should be noted that the above embodiments have been described with one VLC encoder
and decoder only, but it is clear that this concept can be generalized to the use of two and
more VLC encoders and decoders to be interleaved with the PIPE coders.
Although some aspects have been described in the context of an apparatus, it is clear that
these aspects also represent a description of the corresponding method, where a block or
device corresponds to a method step or a feature of a method step. Analogously, aspects
described in the context of a method step also represent a description of a corresponding
block or item or feature of a corresponding apparatus. Some or all of the method steps may
be executed by (or using) a hardware apparatus, like for example, a microprocessor, a
programmable computer or an electronic circuit. In some embodiments, some one or more
of the most important method steps may be executed by such an apparatus.

The inventive encoded/compressed signals can be stored on a digital storage medium or
can be transmitted on a transmission medium such as a wireless transmission medium or a
wired transmission medium such as the Internet.
Depending on certain implementation requirements, embodiments of the invention can be
implemented in hardware or in software. The implementation can be performed using a
digital storage medium, for example a floppy disk, a DVD, a Blue-Ray, a CD, a ROM, a
PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable
control signals stored thereon, which cooperate (or are capable of cooperating) with a
programmable computer system such that the respective method is performed. Therefore,
the digital storage medium may be computer readable.
Some embodiments according to the invention comprise a data carrier having
electronically readable control signals, which are capable of cooperating with a
programmable computer system, such that one of the methods described herein is
performed.
Generally, embodiments of the present invention can be implemented as a computer
program product with a program code, the program code being operative for performing
one of the methods when the computer program product runs on a computer. The program
code may for example be stored on a machine readable carrier.
Other embodiments comprise the computer program for performing one of the methods
described herein, stored on a machine readable carrier.
In other words, an embodiment of the inventive method is, therefore, a computer program
having a program code for performing one of the methods described herein, when the
computer program runs on a computer,
A further embodiment of the inventive methods is, therefore, a data carrier (or a digital
storage medium, or a computer-readable medium) comprising, recorded thereon, the
computer program for performing one of the methods described herein.
A further embodiment of the inventive method is, therefore, a data stream or a sequence of
signals representing the computer program for performing one of the methods described
herein, The data stream or the sequence of signals may for example be configured to be
transferred via a data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example a computer, or a
programmable logic device, configured to or adapted to perform one of the methods
described herein.
A further embodiment comprises a computer having installed thereon the computer
program for performing one of the methods described herein.
In some embodiments, a programmable logic device (for example a field programmable
gate array) may be used to perform some or all of the functionalities of the methods
described herein. In some embodiments, a field programmable gate array may cooperate
with a microprocessor in order to perform one of the methods described herein. Generally,
the methods are preferably performed by any hardware apparatus.
The above described embodiments are merely illustrative for the principles of the present
invention. It is understood that modifications and variations of the arrangements and the
details described herein will be apparent to others skilled in the art. It is the intent,
therefore, to be limited only by the scope of the impending patent claims and not by the
specific details presented by way of description and explanation of the embodiments
herein.

We Claim:
1. Entropy encoding apparatus comprising
a decomposer (136) configured to convert a sequence (138) of syntax elements
having a value range which is sub-divided into a sequence of N partitions (1401-3)
into a sequence (106) of source symbols (106) by individually decomposing each of
at least a subgroup of the syntax elements into a respective number n of source
symbols Si with i=1.. .n, the respective number n of source symbols depending on as
to which of the sequence of N partitions (1401-3) a value z of the respective syntax
elements falls into, so that a sum of values of the respective number of source
symbols Si yields z, and, if n>1, for all i=1...n-1, the value of Si corresponds to a
range of the ith partition;
a subdivider (100) configured to subdivide the sequence (106) of source symbols
into a first subsequence (108) of source symbols and a second subsequence (110) of
source symbols such that all source symbols sx with x being member of a first
subset of {1...N} are contained within the first subsequence (108) and all source
symbols sy with y being member of a second subset of {1.. .N} being disjoint to the
first subset, are contained within the second subsequence (110);
a VLC encoder (102) configured to symbol-wisely encode the source symbols of
the first subsequence (108); and
a probability interval partitioning entropy or arithmetic encoder (104) configured to
encode the second subsequence (110) of source symbols.
2. Entropy encoding apparatus according to claim 1, wherein the values z of the
subgroup of the syntax elements are absolute values.
3. Entropy encoding apparatus according to claim 1 or 2, wherein the second subset is
{1} with the sequence of n partitions being arranged such that a p1 partition covers
higher values of the value range than a qth partition for all p,q e {1 ..N} with p>q.
4. Entropy encoding apparatus according to claim 3, wherein N = 3.
5. Entropy encoding apparatus according to claim 4, wherein the first subset is {2,3}
with the a VLC encoder (102) configured to use a Golomb-Rice code to symbol-

wisely encode the source symbols S2, and a Exp-Golomb Code to symbol-wisely
encode the source symbols S3.
6. Entropy encoding apparatus according to claim 2, wherein 2 is element of the first
subset with the a VLC encoder (102) being configured to use a Golomb-Rice code
to symbol-wisely encode the source symbols S2 and adapt a Golomb-Rice
parameter of the Golomb-Rice code according to previously encoded symbols.
7. Entropy encoding apparatus according to claim 2, wherein the decomposer is
configured to adapt one or more of limits between the partitions according to
previously encoded source symbols.
8. Entropy encoding apparatus according to any of claims 1 to 7, wherein the
subgroup of the syntax elements encompass absolute transform coefficient levels of
absolute transform coefficients of transform blocks of a picture with the absolute
transform coefficient levels of a respective transform block being arranged within
the sequence (138) of syntax elements in accordance with a scan path leading
through the absolute transform coefficients of the respective transform blocks,
wherein the decomposer is configured to adapt one or more of limits between the
partitions during decomposing the absolute transform coefficient levels of the
absolute transform coefficients of a respective transform block depending on
already encoded absolute transform coefficient levels of absolute transform
coefficients of the respective transform blocks preceding in the scan order or
depending on a position of the absolute transform coefficient level currently to be
decomposed in the scan order, or based on an evaluation of the already
reconstructed absolute transform coefficient levels of transform coefficients
neighboring - either spatially or in scan order - the position of the absolute
transform coefficient level currently to be decomposed.
9. Entropy encoding apparatus according to any of claims 1 to 8, wherein the syntax
elements are of different type and the decomposer (136) is configured to perform
the individual decomposing depending on the type of the syntax elements.
10. Entropy encoding apparatus according to any of claims 1 to 9, wherein the
probability interval partitioning entropy or arithmetic encoder (104) is a probability
interval partitioning entropy encoder configured to encode the second subsequence
(110) of source symbols, represented in form of a sequence (124) of alphabet
symbols, the probability interval partitioning entropy encoder comprising

an assigner (114) configured to assign a measure for an estimate of a
probability distribution among the possible values the respective alphabet
symbols may assume, to each alphabet symbol of the sequence (124) of
alphabet symbols based on information contained within previous alphabet
symbols of the sequence (124) of alphabet symbols;
a plurality of entropy encoders (116) each of which is configured to convert
the alphabet symbols forwarded to the respective entropy encoder into a
respective partial second bit stream (118); and
a selector (120) configured to forward each alphabet symbol to a selected
one of the plurality of entropy encoders (118), the selection depending on
the measure assigned to the respective alphabet symbol.
11. Entropy encoding apparatus according to claim 10, wherein the syntax elements are
of different type and the subdivider (100) is configured to perform the subdivision
depending on the type of the syntax elements.
12. Entropy encoding apparatus according to any of claims 10 to 11, further comprising
a symbolizer (122) configured to individually map each source symbol of the
second subsequence (110) into a respective partial sequence of alphabet symbols
together forming the sequence (124) of alphabet symbols.

12. Entropy encoding apparatus encoding apparatus according to claim 11, wherein the
symbolizer (122) and the probability interval partitioning entropy encoder (104) are
configured such that the alphabet symbols are binary symbols.
13. Entropy encoding apparatus according to any of claims 10 to 12 wherein the
sequence (124) of alphabet symbols are of a binary alphabet, and the assigner (114)
is configured such that the estimate of the probability distribution consists of a
measure for an estimate of a probability of a less probable or more probable bin
value and an identifier specifying an estimate for which of the two possible bin
values represents the less probable or more probable bin value.
14. Entropy encoding apparatus according to any of claims 10 to 15 wherein the
assigner (114) is configured to assign a context to each alphabet symbol of the
sequence of alphabet symbols based on the information contained within previous

alphabet symbols of the sequence of alphabet symbols with each context having a
respective probability distribution estimate associated therewith, and to adapt the
probability distribution estimate of each context to an actual symbol statistic based
on symbol values of previous alphabet symbols to which the respective context is
assigned, and to determine the measure for the estimate of the probability
distribution for each alphabet symbol based on the probability distribution estimate
associated with the context assigned to the respective alphabet symbol.
15. Entropy encoding apparatus according to claim 14, wherein the assigner (114) is
configured to, in determining the measure for the estimate of the probability
distribution for each alphabet symbol, quantize the probability distribution estimate
associated with the context assigned to the respective alphabet symbol to one of a
plurality of probability distribution estimate representatives in order to obtain the
measure for the estimate of the probability distribution and wherein the selector
(120) is configured such that a surjective association is defined from the plurality of
probability distribution estimate representatives to the plurality of entropy encoders
(116).
16. Entropy encoding apparatus according to claim 15, wherein the selector (114) is
configured to change a quantization mapping from a range of the probability
distribution estimate to the plurality of probability distribution estimate
representatives in a predetermined deterministic way depending on previous
alphabet symbols of the sequence (124) of alphabet symbols over time.
17. Entropy encoding apparatus according to claim 16, wherein the plurality of entropy
encoders (116) is configured to adapt their way of converting alphabet symbols into
the partial second streams (118) responsive to a change in the quantization
mapping.
18. Entropy encoding apparatus according to claim 16 or 17 wherein the selector (114)
is configured to change the quantization mapping such that bitrates of the partial
second streams (118) into which the entropy encoders (116) convert the alphabet
symbols, are rendered less dispersed.
19. Entropy encoding apparatus according to any of claims 10 to 18, wherein at least
one of the plurality of the entropy encoders (116) has a symbol input buffer
associated therewith, wherein the selector (120) is configured to forward the

alphabet symbols to the at least one entropy encoder (116) via the associated
symbol input buffer.
20. Entropy encoding apparatus according to any of claims 10 to 19 wherein the
plurality of entropy encoders (116) are variable length coders configured to map
alphabet symbol sequences to codewords.
21. Entropy encoding apparatus according to any of claims 10 to 20 wherein each of
the plurality of entropy encoders (116) is a variable length coder configured to map
alphabet symbol sequences of variable lengths to codewords of fixed lengths.
22. Entropy encoding apparatus according to claim 20 or 21 further comprising an
interleaver (128) configured to reserve a sequence of codeword entries for the
codewords within the first bitstream (112) and the partial second streams (118) in a
sequential order depending on an order in which the alphabet symbols of the
sequence of alphabet symbols forwarded by the selector (120) to the plurality of
entropy encoders (116) result in a beginning of a new alphabet symbol sequence to
be mapped to a codeword at the respective entropy encoder (116) and a new source
symbol of the second substream (108) is mapped by the VLC encoder 102,
respectively, and to remove codewords entered into the codeword entries in the
sequential order to obtain a single stream (126) of interleaved codewords from the
first bit stream (112) and partial second streams (118), respectively, wherein each
entropy encoder (116) is configured to sequentially enter its codewords into the
codeword entries reserved for the respective entropy encoder (116), and the selector
(120) is configured to forward the alphabet symbols representing the source
symbols of the second sub-stream (110) in an order maintaining an order in which
the source symbols of the first sub-stream (108) and the second sub-stream(110)
were interspersed within the sequence of source symbols.
23. Entropy encoding apparatus according to claim 22, wherein the plurality of entropy
encoders (116) and the interleaver (128) are configured to intermittently extend
currently forwarded but not yet mapped symbols to valid alphabet symbol
sequences by don't-care alphabet symbols having the currently forwarded but not
yet mapped alphabet symbols as prefix, map the thus extended alphabet symbol
sequences into codewords, enter the thus obtained codewords into the reserved
codeword entries and flush the codeword entries.

24. Entropy encoding apparatus according to claim 23, wherein the plurality of entropy
encoders (116) and the interleaver (128) are configured to perform the
intermittently extending, entering and flushing at events where a number of
reserved codeword entries plus a number of codeword entries having codewords
entered therein fulfils a predetermined criterion.
25. Entropy decoding apparatus comprising
a VLC decoder (200) configured to codeword-wisely reconstruct source symbols of
a first subsequence (204) of source symbols from codewords of a first bitstream
(206);
a probability interval partitioning entropy or arithmetic decoder (202) configured to
reconstruct a second subsequence (208) of source symbols;
a composer (224) configured to compose a sequence (226) of syntax elements
having a value range which is sub-divided into a sequence of N partitions (1401-3)
from the first subsequence (204) of source symbols and the second subsequence
(208) of source symbols by individually composing each syntax element from a
respective number n of source symbols by, for each of at least a subgroup of the
syntax elements, determining the respective number n of source symbols Si with
i=l...n depending on as to which of the sequence of N partitions (1401-3) into
which a value range of the respective syntax elements is sub-divided, a value z of
the respective syntax elements falls into, by summing-up the values of the
respective number of source symbols si from 1 to n as long as the value of si
corresponds to a range of the ith partition so as to obtain the value of the syntax
element z, wherein the composer (224) is configured to retrieve all source symbols
sx with x being member of a first subset of {1.. .N} from the first subsequence (204)
and all source symbols sy with y being member of a second subset of {1.. .N} being
disjoint to the first subset, from the second subsequence (208).
26. Entropy decoding apparatus according to claim 25, wherein the values z of the
subgroup of the syntax elements are absolute values.
27. Entropy decoding apparatus according to claim 25 or 26, wherein the second subset
is {1} with the sequence of N partitions being arranged such that a pth partition
covers higher values of the value range than a qth partition for all p,q ϵ {1..N} with
p>q.

28. Entropy decoding apparatus according to claim 27, wherein N = 3.
29. Entropy encoding apparatus according to claim 28, wherein the first subset is {2,3}
with the a VLC decoder (200) configured to use a Golomb-Rice code to codeword-
wisely reconstruct the source symbols S2, and a Exp-Golomb Code to codeword-
wisely reconstruct the source symbols S3.
30. Entropy encoding apparatus according to claim 25, wherein 2 is element of the first
subset with the a VLC decoder (102) being configured to use a Golomb-Rice code
to codeword-wisely reconstruct the source symbols S2 and adapt a Golomb-Rice
parameter of the Golomb-Rice code according to previously reconstructed source
symbols.
31. Entropy decoding apparatus according to any of claims 25 to 30 further comprising
a recombiner (220) configured to recombine the first subsequence (204) of source
symbols and the second subsequence of source symbols to obtain the sequence
(218) of source symbols.
32. Entropy decoding apparatus according to any of claims 25 to 31, wherein the syntax
elements are of different type and the composer is configured to perform the
individual composing depending on the type of the syntax elements.
33. Entropy decoding apparatus according to any of claims 25 to 32, wherein the
subgroup of the syntax elements encompass absolute transform coefficient levels of
absolute transform coefficients of transform blocks of a picture with the absolute
transform coefficient levels of a respective transform block being arranged within
the sequence (138) of syntax elements in accordance with a scan path leading
through the absolute transform coefficients of the respective transform blocks,
wherein the composer is configured to adapt one or more of limits between the
partitions during composing the absolute transform coefficient levels of the
absolute transform coefficients of a respective transform block depending on
already reconstructed absolute transform coefficient levels of absolute transform
coefficients of the respective transform blocks preceding in the scan order or
depending on a position of the absolute transform coefficient level currently to be
composed in the scan order, or based on an evaluation of the already reconstructed
absolute transform coefficient levels of transform coefficients neighboring - either

spatially or in scan order - the position of the absolute transform coefficient level
currently to be composed.
34. Entropy encoding apparatus according to any of claims 25 to 33, wherein the
composer is configured to adapt one or more of limits between the partitions
according to previously reconstructed source symbols.
35. Entropy encoding apparatus according to claims 26, wherein the composer is
configured to adapt one or more of limits between the partitions according to
previously reconstructed source symbols.
36. Entropy decoding apparatus according to claim 6, wherein the probability interval
partitioning entropy or arithmetic decoder is a probability interval partitioning
entropy decoder configured to reconstruct the second subsequence (110) of source
symbols, represented in form of a sequence (224) of alphabet symbols, and
responsive to alphabet symbol requests sequentially requesting for the alphabet
symbols, the probability interval partitioning entropy decoder comprising:
a plurality of entropy decoders (210), each of which is configured to convert
a respective partial secondstream (216) into alphabet symbols of the
sequence of alphabet symbols;
an assigner (212) configured to assign to each request for an alphabet
symbol of the sequence of alphabet symbols representing the second
subsequence (208) of source symbols to be reconstructed, a measure of an
estimate of a probability distribution among the possible values the
respective alphabet symbol may assume, based on information contained
within previously reconstructed alphabet symbols of the sequence of
alphabet symbols; and
a selector (214) configured to retrieve, for each request for an alphabet
symbol of the sequence of alphabet symbols representing the second
subsequence (208) of source symbols to be reconstructed, the respective
alphabet symbol of the sequence of alphabet symbols from a selected one of
the plurality of entropy decoders (210), the selection depending on the
measure assigned to the respective request for the respective alphabet
symbol,

wherein the first subsequence (204) of source symbols and the second subsequence
(208) of source symbols commonly form a sequence (218) of source symbols.
37. Entropy decoding apparatus according to claim 36, wherein the sequence (218) of
source symbols is a sequence of syntax elements of a parsable bit stream.
38. Entropy decoding apparatus according to claim 37, wherein the syntax elements are
of different type and the first bitstream (206) and the second bit streams (216) are
interleaved with each other into an interleaved bitstream (228), the entropy
decoding apparatus being configured to separate the first bitstream (206) from the
second bit streams (216) depending on the type of the syntax elements.
39. Entropy decoding apparatus according to any of claims 36 to 38, further comprising
a desymbolizer (122) configured to individually re-map, in units of partial
sequences of alphabet symbols, the sequence (124) of alphabet symbols into the
source symbols of the second subsequence (110).
40. Entropy decoding apparatus encoding apparatus according to claim 39, wherein the
desymbolizer (122) and the PIPE decoder (104) are configured such that the
alphabet symbols are binary symbols.
41. Entropy decoding apparatus according to any of claims 36 to 40, wherein the
subsequence of alphabet symbols is of a binary alphabet and the assigner is
configured such that the estimate of the probability distribution consists of a
measure for an estimate of a probability of a less probable or more probable bin
value of the two possible bin values of the binaiy alphabet and an identifier
specifying an estimate for which of the two possible bin values represents the less
probable or more probable bin value.
42. Entropy decoding apparatus according to any of claims 36 to 41, wherein the
assigner (212) is configured to internally assign a context to each request for an
alphabet symbol of the subsequence of alphabet symbols, based on the information
contained within previously reconstructed alphabet symbols of the subsequence of
alphabet symbols with each context having a respective probability distribution
estimate associated therewith, and to adapt the probability distribution estimate for
each context to an actual symbol statistic based on symbol values of previously
reconstructed alphabet symbols to which the respective context is assigned, and to

determine, for each request for an alphabet symbol of the subsequence of alphabet
symbols, the measure for the estimate of the probability distribution for the
respective alphabet symbol of the subsequence of alphabet symbols based on the
probability distribution estimate associated with the context assigned to the
respective alphabet symbol.
43. Entropy decoding apparatus according to claim 42, wherein the assigner (212) is
configured to, in determining the measure for the estimate of the probability
distribution for each request for an alphabet symbol, quantize the probability
distribution estimate associated with the context assigned with the respective
alphabet symbol to one of a plurality of probability distribution estimate
representatives in order to obtain the measure for the estimate of the probability
distribution and wherein the selector is configured such that a surjective association
is defined from the plurality of probability distribution estimate representatives to
the plurality of entropy decoders.
44. Entropy decoding apparatus according to claim 43, wherein the selector is
configured to change a quantization mapping from a range of the probability
distribution estimates to the plurality of probability distribution estimate
representatives in a predetermined deterministic way depending on previously
reconstructed alphabet symbols of the sequence of alphabet symbols, over time.
45. Entropy decoding apparatus according to claim 44, wherein the plurality of entropy
decoders is configured to adapt their way of converting the respective partial
second stream into alphabet symbols responsive to a change in the quantization
mapping.
46. Entropy decoding apparatus according to claims 44 or 45, wherein the selector is
configured to change the quantization mapping such that rates by which the
alphabet symbols are retrieved from the plurality of entropy decoders, are made less
dispersed.
47. Entropy decoding apparatus according to any of claims 36 to 46, wherein at least
one entropy decoder has a symbol output buffer associated therewith, wherein the
selector is configured to retrieve the alphabet symbols from the at least one entropy
decoder via the associated symbol output buffer.

48. Entropy decoding apparatus according to any of claims 36 to 47, wherein the
entropy decoders are variable length decoders configured to map codewords to
alphabet symbol sequences.
49. Entropy decoding apparatus according to claim 48, further comprising a
deinterleaver (230) configured to generate the first and partial secondstreams by
deinterleaving codewords within a single bitstream (228) in an order defined by the
order of the source symbols of the first subsequence (204) and the second
subsequence (208) within the sequence (218) of source symbols.
50. Entropy decoding apparatus according to claim 49, wherein the deinterleaver (230)
is configured to,
whenever a source symbol within the sequence (218) of source symbols currently in
line, belongs to the first subsequence (204), regard a current codeword within single
bitstream (228) as a codeword of the first bitstream (206) and,
whenever a source symbol within the sequence (218) of source symbols currently in
line, belongs to the second subsequence (208), regard a current codeword within
single bitstream (228) as a codeword of a respective one of the partial
secondstreams (216), if any of the alphabet symbols belonging to the current source
symbol necessitates a new mapping of a codeword of the respective partial
secondstreams (216) to a respective alphabet symbol sequence by the entropy
decoder (210) selected depending on the measure assigned to the request for the
respective alphabet symbol, using, if several of such alphabet symbols exist which
belong to the current source symbol, an order among such alphabet symbols, which
depends on the order of the alphabet symbols within the sequence (224) of alphabet
symbols.
51. Entropy encoding method comprising
converting a sequence (138) of syntax elements having a value range which is sub-
divided into a sequence of N partitions (1401-3) into a sequence (106) of source
symbols (106) by individually decomposing each of at least a subgroup of the
syntax elements into a respective number n of source symbols si with i=1...n, the
respective number 11 of source symbols depending on as to which of the sequence of
N partitions (1401-3) a value z of the respective syntax elements falls into, so that a

sum of values of the respective number of source symbols si yields z, and, if n>1,
for all i=1.. .n-1, the value of Si corresponds to a range of the ith partition;
subdividing the sequence (106) of source symbols into a first subsequence (108) of
source symbols and a second subsequence (110) of source symbols such that all
source symbols sx with x being member of a first subset of {1...N} are contained
within the first subsequence (108) and all source symbols sy with y being member
of a second subset of {1 ...N} being disjoint to the first subset, are contained within
the second subsequence (110);
by VLC encoding, symbol-wisely encoding the source symbols of the first
subsequence (108); and
by probability interval partitioning entropy or arithmetic encoding, encoding the
second subsequence (110) of source symbols.
52. Entropy decoding method comprising
by VLC decoding, codeword-wisely reconstructing source symbols of a first
subsequence (204) of source symbols from codewords of a first bitstream (206);
by probability interval partitioning entropy or arithmetic decoding, reconstructing a
second subsequence (208) of source symbols;
composing a sequence (226) of syntax elements having a value range which is sub-
divided into a sequence of N partitions (1401.3) from the first subsequence (204) of
source symbols and the second subsequence (208) of source symbols by
individually composing each syntax element from a respective number n of source
symbols by, for each of at least a subgroup of the syntax elements, determining the
respective number n of source symbols Si with i=1.. .n depending on as to which of
the sequence of N partitions (1401-3) into which a value range of the respective
syntax elements is sub-divided, a value z of the respective syntax elements falls
into, by summing-up the values of the respective number of source symbols Si from
1 to n as long as the value of Si corresponds to a range of the ith partition so as to
obtain the value of the syntax element z, wherein the composing (224) comprises
retrieving all source symbols sx with x being member of a first subset of {1 ...N}
from the first subsequence (204) and all source symbols sy with y being member of

a second subset of {1...N} being disjoint to the first subset, from the second
subsequence (208).
53. A computer program having a program code for performing, when running on a
computer, a method according to claim 51 or 52.