Extracted from wipo site
Arithmetic Encoders, Arithmetic Decoders, Video Encoder, Video Decoder, Methods for Encoding, Methods for Decoding and Computer Program
Technical Field
Embodiments according to the invention create arithmetic encoders.
Further embodiments according to the invention create arithmetic decoders.
Further embodiments according to the invention create video encoders.
Further embodiments according to the invention create video decoders.
Further embodiments according to the invention create methods for encoding a plurality of symbols and methods for decoding a plurality of symbols.
Further embodiments according to the invention create corresponding computer programs.
Generally speaking, embodiments according to the invention create a context model update method using a finite state machine.
Background of the Invention
Arithmetic encoding and decoding is proven to be a valuable tool in the encoding and decoding of audio and video contents and also in the encoding of other types of information, like pictures, neural network coefficients and the like. Embodiments of the invention can be used for all of these applications. For example, it is possible to exploit known occurrence probabilities of binary values (e.g., symbols) in a binary sequence representing a video or audio content (or other types of content) to increase encoding efficiency. In particular, arithmetic encoding can deal with varying probabilities of “0”s and “1”s in an efficient manner, and can adapt to changes of the probabilities in a fine-tuned manner.
However, for arithmetic encoding and decoding to bring an optimal coding efficiency, it is important to have a good information about the probabilities of “0”s and “1”s which well reflects an actual frequency of occurrence.
In order to adapt to the probabilities of “0”s and “1”s (or generally, to adapt to probabilities of the symbols to be encoded), a concept is typically used to adjust boundaries of intervals within a total (current) range of values, to obtain an interval sub-division (for example, such that a full range of values is sub-divided into intervals associated with different binary values or groups of binary values).
In other words, information about the probabilities of different symbols (like “0”s and “1”s) is used to derive an interval size information (or, equivalently, an interval size value) which describes a width of an interval associated with a symbol (wherein a total interval width may, for example, vary over time depending on the encoding or decoding process, for example, due to an interval re-normalization).
Accordingly, there is a need for concepts for the determination of source statistic values (e.g. state variable values) and/or range values (like interval size values) for the interval sub-division (for example, for the sub-division of a total coding interval), which provide a good tradeoff between computational efficiency and liability.

Claims
1. An arithmetic encoder (34;400) for encoding a plurality of symbols (24”, 410) having symbol values,
wherein the arithmetic encoder is configured to derive an interval size information (pk, R*pk;; 432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of one or more symbol values to be encoded on the basis of a plurality of state variable values (sik; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110; 1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously encoded symbol values with different adaptation time constants,
wherein the arithmetic encoder is configured to map a first state variable value (sk1), or a scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, using a lookup-table (LUT1) and to map a second state variable value (sk2), or a scaled and/or rounded version (⎣sk2* ak2⎦ ) thereof using the lookup-table (LUT1) ,
in order to obtain the interval size information describing an interval size for the arithmetic encoding of one or more symbols to be encoded.
2. An arithmetic encoder according to claim 1,
wherein the arithmetic encoder is configured to map the first state variable value, or the scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, onto a first probability value (pk1) using the look-up table, and
wherein the arithmetic encoder is configured to map the second state variable value, or the scaled and/or rounded version (⎣sk2* ak2 ⎦ ) thereof, onto a second probability value (pk2) using the look-up table, and
wherein the arithmetic encoder is configured to obtain a combined probability value (pk] using the first probability value and the second probability value.
3. The arithmetic encoder according to one of claims 1 to 2,
wherein the arithmetic encoder is configured to change the state variable value into a first direction if a symbol to be encoded takes a first value, and to change the state variable value into a second direction if a symbol to be encoded takes a second value which is different from the first value,
wherein the arithmetic encoder is configured to determine an entry of the lookup-table to be evaluated in dependence on an absolute value of a respective state variable value.
4. The arithmetic encoder according to claim 3,
wherein the arithmetic encoder is configured to set a first probability value (pk1) to a value provided by the lookup table if the first state variable value takes a first sign, and
wherein the arithmetic encoder is configured to set the first probability value (pk1) to a value obtained by subtracting a value provided by the lookup table from a predetermined value if the first state variable value takes a second sign.
5. The arithmetic encoder according to one of claims 1 to 4,
wherein the arithmetic encoder is configured to determine two or more probability values pki according to wherein LUT1 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein ski is an i-th state variable value; and
wherein aki is a weighting value associated with the i-th state variable value.
6. The arithmetic encoder according to one of claims 1 to 4,
wherein the arithmetic encoder is configured to determine two or more probability values pki according to wherein LUT1 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein ski is an i-th state variable value; and
wherein aki is a weighting value associated with the i-th state variable value.
7. The arithmetic encoder according to one of claims 1 to 6,
wherein the arithmetic encoder is configured to obtain a combined probability value pk on the basis of a plurality of probability values pki according to wherein N is a number of probability values considered; and
wherein bki is a weighting value
8. The arithmetic encoder according to one of claims 1 to 7,
wherein the arithmetic encoder is configured to map the first state variable value, or the scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, onto a first subinterval width value (R*pk1) using a two-dimensional look-up table, entries of which are addressed in dependence on the first state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol,
wherein the arithmetic encoder is configured to map the second state variable value, or the scaled and/or rounded version (⎣sk2* ak2 ⎦ ) thereof, onto a second subinterval width value (R*pk2) using the two-dimensional look-up table, entries of which are addressed in dependence on the second state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol ,
wherein the arithmetic encoder is configured to obtain a combined subinterval width value using the first subinterval width value and the second subinterval width value.
9. The arithmetic encoder according to claim 8,
wherein the two-dimensional look-up table is representable as a dyadic product between a first one-dimensional vector entries of which comprise probability values for different value intervals of a value domain for the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦; |sk| • ak) thereof, and
a second one-dimensional vector (Qr2(R)) entries of which comprise quantization levels for the coding interval size information.
10. The arithmetic encoder according to claim 8, wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a base lookup table (Base TabLPS), wherein a first group of the elements of the two-dimensional lookup-table are identical to elements of the base lookup-table or are rounded versions of elements of the base lookup table, and
wherein a second group of the elements of the two-dimensional lookup-table are scaled and rounded versions of elements of the base lookup-table.
11. The arithmetic encoder according to claim 10,
wherein the second group of elements of the two-dimensional lookup-table are right-shifted versions of elements of the base-lookup table.
12. The arithmetic encoder according to claim 10 or 11,
wherein a probability index (Gp2(pLPS); i) determines whether an element of the first group of elements of the two-dimensional lookup table or an element of a second group of elements of the two-dimensional lookup table is evaluated,
wherein a first range of probability indices is associated with elements of the first group of elements, and
wherein a second range of probability indices is associated with elements of the second group of elements;
13. The arithmetic encoder according to claim 12,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the element of two-dimensional lookup table.
14. The arithmetic encoder according to one of claims 9 to 13,
wherein the arithmetic encoder is configured to obtain an element of the two-dimensional lookup-table (RangTabLPS) according to
RangeTabLPS[i][j]=Scal(BaseTabLPS[i%μ][j] , ⎣i/μ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ;
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
15. The arithmetic encoder according to claim 8,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a probability table (probTabLPS),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein elements of the two-dimensional lookup-table for a probability value which is not in the set of a plurality of probability values and/or for a coding interval size which is different from the given coding interval size are derived from the probability table using a scaling.
16. The arithmetic encoder according to claim 15,
wherein elements of the two-dimensional lookup-table are obtained
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of probability values or not.
17. The arithmetic encoder according to claim 16,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor used in the second scaling and/or
wherein the coding interval size determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
18. The arithmetic encoder according to claim 15 or 16 or 17,
wherein the arithmetic encoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = Scal(⎣probTabLPS[i% μ] • Qr2(R)⎦, ⎣i/μ⎦)
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
19. The arithmetic encoder according to claim 15,
wherein elements of the two-dimensional lookup-table are obtained using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on whether
an element associated with a current probability value is included in the set of probability values or not and using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
20. The arithmetic encoder according to claim 19,
wherein a division residual ( ⎣i%μ⎦ ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor
used in the first scaling; and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
21. The arithmetic encoder according to claim 15 or 19 or 20,
wherein the arithmetic encoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = ⎣Scal(probTabLPS[i % μ], ⎣i/μ⎦) • Qr2(R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
22. The arithmetic encoder according to one of claims 8 to 21,
wherein the two-dimensional look-up table is representable as a dyadic product between
a first one-dimensional vector entries of which comprise probability values for different value intervals of a value domain for the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ; ⎣|sk| • ak⎦) thereof, and
a second one-dimensional vector (Qr2(R )) entries of which comprise quantization levels for the coding interval size information.
23. The arithmetic encoder according to one of claims 1 to 22,
wherein the arithmetic encoder is configured to
compute from the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, first and second subinterval width values (R*pk), respectively, by mapping the first and second state variable values (sk), or a scaled and/or rounded version thereof (⎣sk2* ak2⎦ ) using a one-dimensional look-up table (LUT4) entries of which comprise probability values for different value intervals of a value domain for the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, onto a first and second probability value, and
quantizing a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol onto a quantization level;
determine products between the first and second probability value, on the one hand, and the quantization level, and
obtaining a combined subinterval width value using the first subinterval width value and the second subinterval width value .
24. The arithmetic encoder according to claim 23,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
25. The arithmetic encoder according to claim 23,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information R by Qr2(R ) = (⎣R • 2-u⎦ + v) • 2-w, where u, v and w are parameters.
26. The arithmetic encoder according to any of claims 24 to 25,
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
27. The arithmetic encoder according to any of claims 23 to 26,
wherein different value intervals of the value domain for the first and second state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
28. The arithmetic encoder according to claim 27,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
29. An arithmetic encoder (34;400) for encoding a plurality of symbols (24", 410) having symbol values,
wherein the arithmetic encoder is configured to derive an interval size information (pk, R*pk; 432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of one or more symbol values to be encoded on the basis of a plurality of state variable values (sik; 642,644; 710; 810;910;1010a, 1010b; 1082a, 1082b;1110; 1210;1310; 1410; 1510;1632,1642;1732,1742), which represent statistics of a plurality of previously encoded symbol values with different adaptation time constants,
wherein the arithmetic encoder is configured to derive a combined state variable value (sk;751a;893;1132) one the basis of the plurality of state variable values (sik), and
wherein the arithmetic encoder is configured to map the combined state variable value (sk), or a scaled and/or rounded version thereof (⎣sk2* ak2;⎦753;) using a look-up table, in order to obtain the interval size information describing an interval size for the arithmetic encoding of one or more symbols to be encoded.
30. The arithmetic encoder according to claim 29,
wherein the arithmetic encoder is configured to determine a weighted sum of state variable values, in order to obtain the combined state variable value.
31. The arithmetic encoder according to claim 29 or according to claim 30,
wherein the arithmetic encoder is configured to determine a sum of rounded values
which are obtained by rounding products of state variable values and associated weight values in order to obtain the combined state variable value (sk).

32. The arithmetic encoder according to one of claims 29 to 31,
wherein the arithmetic encoder is configured to determine the combined state variable value sk according to wherein sk2 are state variable values,wherein N is a number of state variable values considered,
wherein ⎣ . ⎦ is a floor operator,
wherein dki are weighting values associated with the state variable values,
33. The arithmetic encoder according to one of claims 29 to 32,
wherein the arithmetic encoder is configured to change the state variable value into a first direction if a symbol to be encoded takes a first value, and to change the state variable value into a second direction if a symbol to be encoded takes a second value which is different from the first value, and
wherein the arithmetic encoder is configured to determine an entry of the lookup-table to be evaluated in dependence on an absolute value of the combined state variable value.
34. The arithmetic encoder according to claim 33,
wherein the arithmetic encoder is configured to set a probability value (pk) to a value provided by the lookup table if the combined state variable value takes a first sign, and
wherein the arithmetic encoder is configured to set the probability value (pk) to a value obtained by subtracting a value provided by the lookup table from a predetermined value if the combined state variable value takes a second sign.
35. The arithmetic encoder according to one of claims 29 to 34,
wherein the arithmetic encoder is configured to determine a combined probability value pk according to wherein LUT2 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein sk is a combined variable value; and
wherein ak is a weighting value associated with the combined state variable value.
36. The arithmetic encoder according to one of claims 29 to 34,
wherein the arithmetic encoder is configured to determine a combined probability value pk according to wherein LUT2 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein sk is a combined variable value; and
wherein ak is a weighting value associated with the combined state variable value.
37. The arithmetic encoder according to one of claims 29 to 36,
wherein the arithmetic encoder is configured to map the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, onto a subinterval width value (R*pk) using a two-dimensional look-up table, entries of which are addressed in dependence on the combined state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol.
38. The arithmetic encoder according to claim 37,
wherein the two-dimensional look-up table is representable as a dyadic product between
a first one-dimensional vector entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version ( ⎣sk* ak ⎦; |sk| • ak) thereof, and
a second one-dimensional vector (Qr2(R )) entries of which comprise quantization levels for the coding interval size information.
39. The arithmetic encoder according to claim 37,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a base lookup table (Base TabLPS),
wherein a first group of the elements of the two-dimensional lookup-table are identical to elements of the base lookup-table or are rounded versions of elements of the base lookup table, and
wherein a second group of the elements of the two-dimensional lookup-table are scaled and rounded versions of elements of the base lookup-table.
40. The arithmetic encoder according to claim 39,
wherein the second group of elements of the two-dimensional lookup-table are right-shifted versions of elements of the base-lookup table.
41. The arithmetic encoder according to claim 39 or 40,
wherein a probability index (Qp2(pLPS); i) determines whether an element of the first group of elements of the two-dimensional lookup table or an element of a second group of elements of the two-dimensional lookup table is evaluated,
wherein a first range of probability indices is associated with elements of the first group of elements, and
wherein a second range of probability indices is associated with elements of the second group of elements.
42. The arithmetic encoder according to claim 41,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the element of two-dimensional lookup table.
43. The arithmetic encoder according to one of claims 38 to 42,
wherein the arithmetic encoder is configured to obtain an element of the two-dimensional lookup-table (RangTabLPS) according to
RangeTabLPS[i][j]=Scal(BaseTabLPS[i%μ][j] , ⎣i/μ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ;
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
44. The arithmetic encoder according to claim 37,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a probability table (probTabLPS),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein elements of the two-dimensional lookup-table for a probability value which is not in the set of a plurality of probability values and/or for a coding interval size which is different from the given coding interval size are derived from the probability table using a scaling.
45. The arithmetic encoder according to claim 44,
wherein elements of the two-dimensional lookup-table are obtained
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of probability values or not.
46. The arithmetic encoder according to claim 45,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling;
and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor used in the second scaling;and/or
wherein the coding interval size determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
47. The arithmetic encoder according to claim 44 or 45 or 46,
wherein the arithmetic encoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = Scal(⎣probTabLPS[i % μ] • Qr2(R)⎦, ⎣i/μ⎦)
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
48. The arithmetic encoder according to claim 44,
wherein elements of the two-dimensional lookup-table are obtained using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on whether an element associated with a current probability value is included in the set of probability values or not and using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
49. The arithmetic encoder according to claim 48,
wherein a division residual (⎣i%μ⎦ ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor used in the first scaling;

and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
50. The arithmetic encoder according to claim 44 or 48 or 49,
wherein the arithmetic encoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = ⎣Scal(probTabLPS[i % μ], ⎣i/μ⎦) • Qr2 (R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x.y) is a scaling function.
51. The arithmetic encoder according to one of claims 29 to 50,
wherein the arithmetic encoder is configured to compute from the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, a subinterval width value
(R*pk) by
mapping the combined state variable value (sk), or a scaled and/or rounded version thereof (⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) using a one-dimensional look-up table (LUT4) entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) thereof, onto a combined probability value, and
quantizing a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol onto a quantization level;
determine a product between the combined probability value and the quantization level.
52. The arithmetic encoder according to claim 51,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
53. The arithmetic encoder according to claim 51,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information R by Qr2(R ) = (⎣R • 2-u⎦ + v) • 2-w, where u, v and w are parameters.
54. The arithmetic encoder according to any of claims51 to 53,
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
55. The arithmetic encoder according to any of claims 51 to 54,
wherein different value intervals of the value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
56. The arithmetic encoder according to claim 55,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
57. The arithmetic encoder according to one of claims 29 to 56,
wherein the lookup-table defines an exponential decay.
58. The arithmetic encoder according to one of claims 29 to 57,
wherein the arithmetic encoder is configured to update the plurality of variable state values according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values,
wherein A is
or deviates therefrom merely for one or more
extreme values of its argument by zero setting or magnitude reduction to avoid the updated leaving a predetermined value range,
where are predetermined parameters.

59. The arithmetic encoder according to claim 58,
configured to derive by table look-up or computationally.

60. An arithmetic encoder (34;400) for encoding a plurality of symbols (24”, 410) having symbol values,
wherein the arithmetic encoder is configured to determine one or more state variable values (s1k, s2k; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110;1210;1310;
1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously encoded symbol values, and
wherein the arithmetic encoder is configured to derive an interval size information (pk, R*pk; 432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of one or more symbol values to be encoded on the basis of the one or more state variable values (sik), which represent statistics of a plurality of previously encoded symbol values,
wherein the arithmetic encoder is configured to update a first state variable value (sk1) in dependence on a symbol to be encoded and using a look-up table (A).
61. The arithmetic encoder according to claim 60,
wherein the arithmetic encoder is configured to update a second state variable value (sk2) in dependence on a symbol to be encoded and using the look-up table (A).
62. The arithmetic encoder according to claim 60 or claim 61,
wherein the arithmetic encoder is configured update the first state variable value and the second state variable values using different adaptation time constants.
63. The arithmetic encoder according to claim 60 or claim 61 or claim 62,
wherein the arithmetic encoder is configured to selectively increase or decrease a previous state variable value by a value determined using the look-up table in dependence on whether a symbol to be encoded takes a first value or a second value which is different from the first value.
64. The arithmetic encoder according to one of claims 60 to 63,
wherein the arithmetic encoder is configured to increase a previous state variable value by a comparatively larger value in case that the previous state variable value is negative when compared to a case that the previous state variable value is positive if a symbol to be encoded takes a first value; and
wherein the arithmetic encoder is configured to decrease a previous state variable value by a comparatively larger value in case that the previous state variable value is positive when compared to a case that the previous state variable value is negative if a symbol to be encoded takes a second value which is different from the first value.
65. The arithmetic encoder according to one of claims 60 to 64,
wherein the arithmetic encoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the first state variable value in dependence on a sum of a predetermined offset value (z) and a previously computed first state variable value
or a scaled and/or rounded version thereof, if a symbol to be encoded
takes a first value; and
wherein the arithmetic encoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the first state variable value in dependence on a sum of a predetermined [offset value (z) and a in inversed version of a previously
computed first state variable value, or a scaled and/or rounded version
thereof, if a symbol to be encoded takes a second value.
66. The arithmetic encoder according to one of claims 60 to 65,
wherein the arithmetic encoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the second state variable value in dependence on a sum of a predetermined offset value (z) and a previously computed second state variable value
or a scaled and/or rounded version thereof, if a symbol to be
encoded takes a first value; and
wherein the arithmetic encoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the second state variable value in dependence on a sum of a predetermined offset value (z) and a in inversed version of a previously

computed second state variable value, or a scaled and/or rounded version
thereof, if a symbol to be encoded takes a second value.
67. The arithmetic encoder according to one of claims 60 to 66,
wherein the arithmetic encoder is configured to apply a first scaling value (mk1), to scale the previously computed first state variable value (sk1), when determining an index of an entry of the lookup table to be evaluated when updating the first state variable value, and
wherein the arithmetic encoder is configured to apply a second scaling value (mk2), to scale the previously computed second state variable value (sk2), when determining an index of an entry of the lookup table to be evaluated when updating the second state variable value, wherein the first scaling value is different from the second scaling value.
68. The arithmetic encoder according to one of claims 60 to 67,
wherein the arithmetic encoder is configured to scale a value returned by an evaluation of the lookup table using a first scaling value when updating the first state variable value,
wherein the arithmetic encoder is configured to scale a value returned by an evaluation of the lookup table using a second scaling value when updating the second state variable value,
wherein the first scaling value is different from the second scaling value.
69. The arithmetic encoder according to one of claims 60 to 68,
wherein the arithmetic encoder is configured to determine one or more updated state variable values according to

If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
70. The arithmetic encoder according to one of claims 60 to 68,
wherein the arithmetic encoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
71. The arithmetic encoder according to one of claims 60 to 68,
wherein the arithmetic encoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
72. The arithmetic encoder according to one of claims 60 to 68
wherein the arithmetic encoder is configured to determine one or more updated state variable values according to

If symbol to be encoded is 1, If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
73. The arithmetic encoder according to one of claims 69 to 72,
wherein the entries of A decrease monotonically with increasing lookup table index.
74. The arithmetic encoder according to claim 69 or 70 or 71 or 72 and 73,
wherein A is

or deviates therefrom merely for one or more extreme values of its argument by zero setting or magnitude reduction to avoid the updated
leaving a predetermined value range, where are predetermined parameters.

75. The arithmetic encoder according to one of claims 60 to 74,
wherein a last entry of the lookup table is equal to zero.
76. The arithmetic encoder according to one of claims 60 to 75,
wherein the arithmetic encoder is configured to apply a clipping operation to the updated state variable values, to keep the updated and clipped state variable values within a predetermined range of values.
77. The arithmetic encoder according to claim 76,
wherein the arithmetic encoder is configured to apply a clipping operation according to

to the updated state variable values,
wherein is a maximum allowed value for and
wherein is a minimum allowed value for

78. The arithmetic encoder according to one of claims 60 to 77,
wherein the arithmetic encoder is configured to apply different scaling values for different context models.
79. The arithmetic encoder according to one of claims 60 to 78,
wherein the arithmetic encoder is configured to obtain the interval size information as defined in one of claims 1 to 55.
80. An arithmetic encoder (34;400) for encoding a plurality of symbols (24”, 410) having symbol values,
wherein the arithmetic encoder is configured to derive an interval size value ( RLPS;432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of one or more symbol values to be encoded on the basis of one or more state variable values (sik; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110; 1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously encoded symbol values,
wherein the arithmetic encoder is configured to determine the interval size value (RLPS) using a base lookup table (Base TabLPS),
wherein the arithmetic encoder is configured to determine the interval size value (RLPS) such that a determined interval size value is identical to an element of the base lookup table or is a rounded version of an element of the base lookup table if a probability index (i; 852; 1332; 1432; 1532), which is obtained on the basis of the one or more state variable values, is within a first range, and such that a determined interval size value is obtained using a scaling and rounding of an element of the base lookup table if the probability index is within a second range; and
wherein the arithmetic encoder is configured to perform the arithmetic encoding of one or more symbols using the interval size value (RLPS).
81. The arithmetic encoder according to claim 80,
wherein the arithmetic encoder is configured to determine the interval size value, such that the determined interval size value (RLPS) is a right-shifted version of an element of the base-lookup table if the probability index is within the second range.
82. The arithmetic encoder according to claim 80 or 81,
wherein the probability index (Qp2(pLPS)) determines whether an element of the lookup table is provided as the interval size value (RLPS), or whether an element of the lookup table is scaled and rounded to obtain the interval size value (RLPS)•
83. The arithmetic encoder according to one of claims 80 to 82,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the interval size value.
84. The arithmetic encoder according to one of claims 80 to 83,
wherein the arithmetic encoder is configured to obtain the interval size value RXPS according to
RXPS=Scal(BaseTabLPS[i%μ][j] , ⎣ i/μ ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
85. An arithmetic encoder (34;400) for encoding a plurality of symbols (24”, 410) having symbol values,
wherein the arithmetic encoder is configured to derive an interval size value (RLPS; 432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of one or more symbol values to be encoded on the basis of one or more state variable values (sik; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110; 1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously encoded symbol values,
wherein the arithmetic encoder is configured to determine the interval size value (RLPS) using a probability table (Prob TabLPS), on the basis of a probability value (733,735;832,842,852;932,934) derived from the one or more state variable values and on the basis of a coding interval size (R;434;532;712;812;1362;1460;1512),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein the arithmetic encoder is configured to scale an element of the probability table (Prob_TabLPS), to obtain the interval size value (RLPS) if a current probability value is not in the set of a plurality of probability values and/or if a current coding interval size (R) is different from the given coding interval size; and
wherein the arithmetic encoder is configured to perform the arithmetic encoding of one or more symbols using the interval size value (RLPS).
86. The arithmetic encoder according to claim 85,
wherein the arithmetic encoder is configured to obtain an interval size value
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of a plurality of probability values or not.
87. The arithmetic encoder according to claim 86,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result ( ⎣i/μ⎦ ) of a division between the probability index (i) and the first size value determines a scaling factor
used in the second scaling; and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
88. The arithmetic encoder according to claim 86 or 87,
wherein the arithmetic encoder is configured to obtain the interval size value RXPS according to
RXPS = Scal(⎣probTabLPS[i % μ] • Qr2(R)⎦, ⎣i/μ⎦)
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
89. The arithmetic encoder according to claim 85,
wherein the arithmetic encoder is configured to obtain an interval size value
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on whether an element associated with a current probability value is included in the probability value or not, and
- using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
90. The arithmetic encoder according to claim 89,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦ ) of a division between the probability index (i) and the first size value determines a scaling factor used in the first scaling;
and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
91. The arithmetic encoder according to claim 89 or 90,
wherein the arithmetic encoder is configured to obtain the interval size value RXPS according to
RXPS = ⎣Scal(probTabLPS[i % μ], ⎣i/μ⎦) • Qr2(R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
92. An arithmetic decoder (50; 500;1620;1720) for decoding a plurality of symbols
(24”;520;1622;1722) having symbol values,
wherein the arithmetic decoder is configured to derive an interval size value ( RLPS;432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic decoding of one or more symbol values to be decoded on the basis of one or more state variable values (sik; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110; 1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously decoded symbol values,
wherein the arithmetic decoder is configured to determine the interval size value (RLPS) using a base lookup table (Base TabLPS),
wherein the arithmetic decoder is configured to determine the interval size value (RLPS) such that a determined interval size value is identical to an element of the base lookup table or is a rounded version of an element of the base lookup table if a probability index (i; 852;1332;1432;1532), which is obtained on the basis of the one or more state variable values, is within a first range, and such that a determined interval size value is obtained using a scaling and rounding of an element of the base lookup table if the probability index is within a second range; and
wherein the arithmetic decoder is configured to perform the arithmetic decoding of one or more symbols using the interval size value (RLPS).
93. The arithmetic decoder according to claim 92,
wherein the arithmetic decoder is configured to determine the interval size value, such that the determined interval size value (RLPS) is a right-shifted version of an element of the base-lookup table if the probability index is within the second range.
94. The arithmetic decoder according to claim 92 or 93,
wherein the probability index (Qp2(pLPS)) determines whether an element of the lookup table is provided as the interval size value (RLPS), or whether an element of the lookup table is scaled and rounded to obtain the interval size value (RLPS)•
95. The arithmetic decoder according to one of claims 92 to 94,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the interval size value.
96. The arithmetic decoder according to one of claims 92 to 95,
wherein the arithmetic decoder is configured to obtain the interval size value RXPS according to
Rxps=Scal(BaseTabLPS[i%μ][j] , ⎣ i/μ ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
97. An arithmetic decoder (50; 500;1620;1720) for decoding a plurality of symbols
(24”;520;1622;1722) having symbol values,
wherein the arithmetic decoder is configured to derive an interval size value (RLPS;432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic decoding of one or more symbol values to be decoded on the basis of one or more state variable values (sik; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110; 1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously decoded symbol values,
wherein the arithmetic decoder is configured to determine the interval size value (RLPS) using a probability table (ProbTabLPS), on the basis of a probability value derived from the one or more state variable values and on the basis of a coding interval size (R; 434; 532;712;812; 1362; 1460;1512),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein the arithmetic decoder is configured to scale an element of the probability table (Prob_TabLPS), to obtain the interval size value (RLPS) if a current probability value is not in the set of a plurality of probability values and/or if a current coding interval size (R) is different from the given coding interval size; and
wherein the arithmetic decoder is configured to perform the arithmetic decoding of one or more symbols using the interval size value (RLPS).
98. The arithmetic decoder according to claim 97,
wherein the arithmetic decoder is configured to obtain an interval size value
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of a plurality of probability values or not.
99. The arithmetic decoder according to claim 98,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦ ) of a division between the probability index (i) and the first size value determines a scaling factor
used in the second scaling; and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
100. The arithmetic decoder according to claim 98 or 99,
wherein the arithmetic decoder is configured to obtain the interval size value RXPS according to
RXPS = Scal(⎣probTabLPS[i % μ] • Qr2(R)⎦ ⎣i/μ ⎦ )
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
101. The arithmetic decoder according to claim 97,
wherein the arithmetic decoder is configured to obtain an interval size value
- using a first scaling of a selected element (probTabLPS [i%μ]) of the probability table in dependence on whether an element associated with a current probability value is included in the probability value or not, and
- using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
102. The arithmetic decoder according to claim 101,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦ ) of a division between the probability index (i) and the first size value determines a scaling factor used in the first scaling;
and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
103. The arithmetic decoder according to claim 101 or 102,
wherein the arithmetic decoder is configured to obtain the interval size value RXPS according to
RXPS = ⎣Scal(probTabLPS[i% μ], ⎣i/μ⎦) • Qr2(R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
104. An arithmetic encoder (34;400 for encoding a plurality of symbols (24”, 410) having symbol values,
wherein the arithmetic encoder is configured to determine one state variable value (sk), which represents a statistic of a plurality of previously encoded symbol values, and
wherein the arithmetic encoder is configured to compute from the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, a subinterval width value (RLPS; 432;534;620;720;820;820;1020;1084;1120;1320;1420;1520;1662;1762) for an arithmetic encoding of a symbol value to be encoded by
mapping the one state variable value (sk), or a scaled and/or rounded version thereof (⎣sk* ak ⎦; ⎣|sk| • ak⎦) using a one-dimensional look-up table ( probTabLPS[Qp2( ...)]) entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ; ⎣|sk| • ak⎦) thereof, onto a probability value (pik;pk;pLPS;Qp(pLPS)), and
quantizing a coding interval size information (R;434;532;712;812;1362;1460;1512) describing a size of a coding interval of the arithmetic encoding before the arithmetic encoding of the symbol value to be encoded onto a quantization level (Qr2(R): 762;862);
determine a product between the probability value and the quantization level, wherein the arithmetic encoder is configured to perform a state variable value update in dependence on the symbol value to be encoded.
105. The arithmetic encoder according to claim 104,
wherein the arithmetic encoder is configured to derive as the one state variable value (sk) a combined state variable value one the basis of a plurality of state variable values (sik) , which represent statistics of the plurality of previously encoded symbol values with different adaptation time constants.
106. The arithmetic encoder according to claim 105,
wherein the arithmetic encoder is configured to determine a weighted sum of state variable values, in order to obtain the combined state variable value.
107. The arithmetic encoder according to claim 105 or according to claim 106,
wherein the arithmetic encoder is configured to determine a sum of rounded values
which are obtained by rounding products of state variable values and

associated weight values in order to obtain the combined state variable value (sk).

108. The arithmetic encoder according to one of claims 105 to 107,
wherein the arithmetic encoder is configured to determine the combined state variable value sk according to

wherein sk2 are state variable values,
wherein N is a number of state variable values considered,
wherein ⎣ . ⎦ is a floor operator,
wherein dki are weighting values associated with the state variable values.
109. The arithmetic encoder according to one of claims 105 to 108,
wherein the arithmetic encoder is configured to, in performing the state variable value update, update the plurality of state variable values according to

If symbol to be encoded is 1.
If symbol to be encoded is 0

wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values,
wherein A is
or deviates therefrom merely for one or more
extreme values of its argument by zero setting or magnitude reduction to avoid the updated leaving a predetermined value range,
where are predetermined parameters.

110. The arithmetic encoder according to claim 109,
configured to derive by table look-up or computationally.

111. The arithmetic encoder according to one of claims 104 to 108,
wherein the arithmetic encoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
112. The arithmetic encoder according to one of claims 104 to 108,
wherein the arithmetic encoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0
wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
113. The arithmetic encoder according to one of claims 104 to 108,
wherein the arithmetic encoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
114. The arithmetic encoder according to any of claims 104 to 110,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
115. The arithmetic encoder according to any of claims 104 to 110,
wherein the arithmetic encoder is configured to perform the quantizing the coding interval size information R by Qr2(R) = (⎣R • 2-u⎦ + v) • 2-w, where u, v and w are parameters.
116. The arithmetic encoder according to any of claims 104 to 115,
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
117. The arithmetic encoder according to any of claims 104 to 116,
wherein different value intervals of the value domain for the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
118. The arithmetic encoder according to claim 117,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
119. An arithmetic decoder for decoding a plurality of symbols having symbol values,
wherein the arithmetic decoder is configured to derive an interval size information (pk, R*pk) for an arithmetic decoding of one or more symbol values to be decoded on the basis of a plurality of state variable values (sik), which represent statistics of a plurality of previously decoded symbol values with different adaptation time constants,
wherein the arithmetic decoder is configured to map a first state variable value (sk1), or a scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, using a lookup-table (LUT1) and to map a second state variable value (sk2), or a scaled and/or rounded version (⎣sk2* ak2⎦ ) thereof using the lookup-table (LUT1), in order to obtain the interval size information describing an interval size for the arithmetic decoding of one or more symbols to be decoded.
120. An arithmetic decoder according to claim 119,
wherein the arithmetic decoder is configured to map the first state variable value, or the scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, onto a first probability value (pk1) using the look-up table, and
wherein the arithmetic decoder is configured to map the second state variable value, or the scaled and/or rounded version (⎣sk2* ak2 ⎦ ) thereof, onto a second probability value (pk2) using the look-up table, and
wherein the arithmetic decoder is configured to obtain a combined probability value (pk) using the first probability value and the second probability value.
121. The arithmetic decoder according to one of claims 119 to 120,
wherein the arithmetic decoder is configured to change the state variable value into a first direction if a decoded symbol takes a first value, and to change the state variable value into a second direction if a decoded symbol takes a second value which is different from the first value,
wherein the arithmetic decoder is configured to determine an entry of the lookup-table to be evaluated in dependence on an absolute value of a respective state variable value.
122. The arithmetic decoder according to claim 121,
wherein the arithmetic decoder is configured to set a first probability value (pk1) to a value provided by the lookup table if the first state variable value takes a first sign, and
wherein the arithmetic decoder is configured to set the first probability value (pk1) to a value obtained by subtracting a value provided by the lookup table from a predetermined value if the first state variable value takes a second sign.
123. The arithmetic decoder according to one of claims 119 to 122,
wherein the arithmetic decoder is configured to determine two or more probability values pki according to

wherein LUT1 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein ski is an i-th state variable value; and
wherein aki is a weighting value associated with the i-th state variable value.
124. The arithmetic decoder according to one of claims 119 to 122,
wherein the arithmetic decoder is configured to determine two or more probability values pki according to

wherein LUT1 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein sk1 is an i-th state variable value; and
wherein aki is a weighting value associated with the i-th state variable value.
125. The arithmetic decoder according to one of claims 119 to 124,
wherein the arithmetic decoder is configured to obtain a combined probability value pk on the basis of a plurality of probability values pki according to

wherein N is a number of probability values considered; and
wherein bki is a weighting value.
126. The arithmetic decoder according to one of claims 119 to 125,
wherein the arithmetic decoder is configured to map the first state variable value, or the scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, onto a first subinterval width value (R*pk1) using a two-dimensional look-up table, entries of which are addressed in dependence on the first state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic decoding before a decoding of a symbol,
wherein the arithmetic decoder is configured to map the second state variable value, or the scaled and/or rounded version (⎣sk1* ak1 ⎦ ) thereof, onto a second subinterval width value (R*pk2) using the two-dimensional look-up table, entries of which are addressed in dependence on the second state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic decoding before a decoding of a symbol,
wherein the arithmetic decoder is configured to obtain a combined subinterval width value using the first subinterval width value and the second subinterval width value.
127. The arithmetic decoder according to claim 126,
wherein the two-dimensional look-up table is representable as a dyadic product between
a first one-dimensional vector entries of which comprise probability values for different value intervals of a value domain for the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ; |sk| • ak ) thereof, and a second one-dimensional vector (Qr2(R)) entries of which comprise quantization levels for the coding interval size information.
128. The arithmetic decoder according to claim 126,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a base lookup table (Base TabLPS),
wherein a first group of the elements of the two-dimensional lookup-table are identical to elements of the base lookup-table or are rounded versions of elements of the base lookup table, and
wherein a second group of the elements of the two-dimensional lookup-table are scaled and rounded versions of elements of the base lookup-table.
129. The arithmetic decoder according to claim 128,
wherein the second group of elements of the two-dimensional lookup-table are right-shifted versions of elements of the base-lookup table.
130. The arithmetic decoder according to claim 128 or 129,
wherein a probability index (Qp2(pLPS); i) determines whether an element of the first group of elements of the two-dimensional lookup table or an element of a second group of elements of the two-dimensional lookup table is evaluated,
wherein a first range of probability indices is associated with elements of the first group of elements, and
wherein a second range of probability indices is associated with elements of the second group of elements;
131. The arithmetic decoder according to claim 130,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the element of two-dimensional lookup table.
132. The arithmetic decoder according to one of claims 126 to 131,
wherein the arithmetic decoder is configured to obtain an element of the two-dimensional lookup-table (RangTabLPS) according to
RangeTabLPS[i][j]=Scal(BaseTabLPS[i%μ][j] , ⎣i/μ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ;
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
133. The arithmetic decoder according to claim 126,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a probability table (probTabLPS),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein elements of the two-dimensional lookup-table for a probability value which is not in the set of a plurality of probability values and/or for a coding interval size which is different from the given coding interval size are derived from the probability table using a scaling.
134. The arithmetic decoder according to claim 133,
wherein elements of the two-dimensional lookup-table are obtained
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of probability values or not.
135. The arithmetic decoder according to claim 134,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor
used in the second scaling; and/or
wherein the coding interval size determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
136. The arithmetic decoder according to claim 133 or 134 or 135,
wherein the arithmetic decoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = Scal(⎣probTabLPS[i % μ] • Qr2(R)⎦, ⎣i/μ⎦)
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
137. The arithmetic decoder according to claim 133,
wherein elements of the two-dimensional lookup-table are obtained using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on whether an element associated with a current probability value is included in the set of probability values or not and using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
138. The arithmetic decoder according to claim 137,
wherein a division residual (⎣i%μ⎦ ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor used in the first scaling;

and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
139. The arithmetic decoder according to claim 133 or 137 or 138,
wherein the arithmetic decoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = ⎣Scal(probTabLPS[i % μ], ⎣i/μ⎦) • Qr2(R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
140. The arithmetic decoder according to one of claims 119 to 139,
wherein the arithmetic decoder is configured to compute from the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, first and second subinterval width values (R*pk), respectively, by
mapping the first and second state variable values (sk), or a scaled and/or rounded version thereof (⎣sk2* ak2⎦ ) using a one-dimensional look-up table (LUT4) entries of which comprise probability values for different value intervals of a value domain for the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, onto a first and second probability value, and
quantizing a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol onto a quantization level;
determine products between the first and second probability value, on the one hand, and the quantization level, and
obtaining a combined subinterval width value using the first subinterval width value and the second subinterval width value.
141. The arithmetic decoder according to claim 140,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
142. The arithmetic decoder according to claim 140,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information R by Qr2 (R) = (⎣R • 2-u⎦ + v) • 2-w , where u, v and w are parameters.
143. The arithmetic decoder according to any of claims 140 to 142
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
144. The arithmetic decoder according to any of claims 140 to 143,
wherein different value intervals of the value domain for the first and second state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
145. The arithmetic decoder according to claim 144,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the first and second state variable values, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
146. An arithmetic decoder (50; 500;1620;1720) for decoding a plurality of symbols
(24”;520;1622;1722) having symbol values,
wherein the arithmetic decoder is configured to derive an interval size information (pk, R*pk; 432;534;620;720;820;820;1020;1084;1120; 1320;1420;1520;1662;1762) for an arithmetic decoding of one or more symbol values to be decoded on the basis of a plurality of state variable values (sik; 642,644; 710;810;910; 1010a, 1010b; 1082a, 1082b; 1110; 1210; 1310; 1410; 1510; 1632, 1642; 1732, 1742), which represent statistics of a plurality of previously decoded symbol values with different adaptation time constants,
wherein the arithmetic decoder is configured to derive a combined state variable value (sk) one the basis of the plurality of state variable values (sik), and
wherein the arithmetic decoder is configured to map the combined state variable value (sk), or a scaled and/or rounded version thereof (⎣sk2* ak2⎦ ) using a look-up table, in order to obtain the interval size information describing an interval size for the arithmetic decoding of one or more symbols to be decoded.
147. The arithmetic decoder according to claim 146,
wherein the arithmetic decoder is configured to determine a weighted sum of state variable values, in order to obtain the combined state variable value.
148. The arithmetic decoder according to claim 146 or according to claim 147,
wherein the arithmetic decoder is configured to determine a sum of rounded values ( which are obtained by rounding products of state variable values and

associated weight values in order to obtain the combined state variable value (sk).

149. The arithmetic decoder according to one of claims 146 to 148,
wherein the arithmetic decoder is configured to determine the combined state variable value sk according to

wherein sk2 are state variable values,
wherein N is a number of state variable values considered,
wherein ⎣ . ⎦ is a floor operator,
wherein dki are weighting values associated with the state variable values,
150. The arithmetic decoder according to one of claims 146 to 149,
wherein the arithmetic decoder is configured to change the state variable value into a first direction if a decoded symbol takes a first value, and to change the state variable value into a second direction if a decoded symbol takes a second value which is different from the first value, and
wherein the arithmetic decoder is configured to determine an entry of the lookup-table to be evaluated in dependence on an absolute value of the combined state variable value.
151. The arithmetic decoder according to claim 150,
wherein the arithmetic decoder is configured to set a probability value (pk) to a value provided by the lookup table if the combined state variable value takes a first sign, and
wherein the arithmetic decoder is configured to set the probability value (pk) to a value obtained by subtracting a value provided by the lookup table from a predetermined value if the combined state variable value takes a second sign.
152. The arithmetic decoder according to one of claims 146 to 151,
wherein the arithmetic decoder is configured to determine a combined probability value pk according to

wherein LUT2 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein sk is a combined variable value; and
wherein ak is a weighting value associated with the combined state variable.
153. The arithmetic decoder according to one of claims 146 to 151,
wherein the arithmetic decoder is configured to determine a combined probability value pk according to

wherein LUT2 is a lookup-table containing probability values;
wherein ⎣ . ⎦ is a floor operator;
wherein sk is a combined variable value; and
wherein ak is a weighting value associated with the combined state variable value.
154. The arithmetic decoder according to one of claims 146 to 152,
wherein the arithmetic decoder is configured to map the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, onto a subinterval width value (R*pk) using a two-dimensional look-up table, entries of which are addressed in dependence on the combined state variable value and in dependence on a coding interval size information describing a size of a coding interval of the arithmetic decoding before a decoding of a symbol.
155. The arithmetic decoder according to claim 154,
wherein the two-dimensional look-up table is representable as a dyadic product between
a first one-dimensional vector entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) thereof, and
a second one-dimensional vector (Qr2(R )) entries of which comprise quantization levels for the coding interval size information.
156. The arithmetic decoder according to claim 154,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a base lookup table (Base TabLPS),
wherein a first group of the elements of the two-dimensional lookup-table are identical to elements of the base lookup-table or are rounded versions of elements of the base lookup table, and
wherein a second group of the elements of the two-dimensional lookup-table are scaled and rounded versions of elements of the base lookup-table.
157. The arithmetic decoder according to claim 156,
wherein the second group of elements of the two-dimensional lookup-table are right-shifted versions of elements of the base-lookup table.
158. The arithmetic decoder according to claim 156 or 157,
wherein a probability index (Qp2(pLPS); i) determines whether an element of the first group of elements of the two-dimensional lookup table or an element of a second group of elements of the two-dimensional lookup table is evaluated,
wherein a first range of probability indices is associated with elements of the first group of elements, and
wherein a second range of probability indices is associated with elements of the second group of elements;
159. The arithmetic decoder according to claim158,
wherein a division residual (i%μ) of a division between the probability index (i) and a first size value and an interval size index determine which element of the base lookup table is used to obtain the element of two-dimensional lookup table.
160. The arithmetic decoder according to one of claims 154 to 159,
wherein the arithmetic decoder is configured to obtain an element of the two-dimensional lookup-table (RangTabLPS) according to
RangeTabLPS[i][j]=Scal(BaseTabLPS[i%μ][j] , ⎣i/μ⎦)
wherein BaseTabLPS is a base lookup table of dimension μ x λ;
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein Seal (x,y) is a scaling function.
161. The arithmetic decoder according to claim 154,
wherein elements of the two-dimensional lookup-table (RangTabLPS) are defined on the basis of a probability table (probTabLPS),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein elements of the two-dimensional lookup-table for a probability value which is not in the set of a plurality of probability values and/or for a coding interval size which is different from the given coding interval size are derived from the probability table using a scaling.
162. The arithmetic decoder according to claim 161,
wherein elements of the two-dimensional lookup-table are obtained
- using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on the coding interval size (R), and
- using a second scaling of a result of the first scaling in dependence on whether an element associated with a current probability value is included in the set of probability values or not.
163. The arithmetic decoder according to claim 162,
wherein a division residual (i%μ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result (⎣i/μ⎦) of a division between the probability index (i) and the first size value determines a scaling factor used in the second scaling;

and/or
wherein the coding interval size determines a multiplicative scaling factor (Qr2(R)) of the first scaling.
164. The arithmetic decoder according to claim 161 or 162 or 163,
wherein the arithmetic decoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = Scal(⎣probTabLPS[i % μ] • Qr2(R)⎦, ⎣i/μ ⎦)
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size;
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
165. The arithmetic decoder according to claim 161,
wherein elements of the two-dimensional lookup-table are obtained using a first scaling of a selected element (probTabLPS[i%μ]) of the probability table in dependence on whether an element associated with a current probability value is included in the set of probability values or not and using a second scaling of a result of the first scaling in dependence on the coding interval size (R).
166. The arithmetic decoder according to claim 165,
wherein a division residual ( ⎣i%μ⎦ ) of a division between a probability index and a first size value determines which element of the probability table is scaled in the first scaling; and/or
wherein an integer division result ( ⎣i/μ⎦ ) of a division between the probability index (i) and the first size value determines a scaling factor used in the first scaling;

and/or
wherein the coding interval size (R) determines a multiplicative scaling factor (Qr2(R)) of the second scaling.
167. The arithmetic decoder according to claim 161 or 165 or 166,
wherein the arithmetic decoder is configured to obtain an element RangeTabLPS[i][j] of the two-dimensional lookup-table
according to
RangeTabLPS[i][j] = ⎣Scal(probTabLPS[i % μ], ⎣i/μ⎦) • Qr2(R)⎦
wherein i is a table index associated with a probability information;
wherein j is a table index associated with an interval size information;
wherein % is a division residual operation;
wherein / is a division operation;
wherein probTabLPS[] is the probability table;
wherein μ is a number of elements of the probability table;
wherein R is an interval size
wherein Qr2(R) is a scaling factor which is dependent on R;
wherein Seal (x,y) is a scaling function.
168. The arithmetic decoder according to one of claims 146 to 167,
wherein the arithmetic decoder is configured to compute from the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, a subinterval width value
(R*pk) by
mapping the combined state variable value (sk), or a scaled and/or rounded version thereof(⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) using a one-dimensional look-up table (LUT4) entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) thereof, onto a combined probability value, and
quantizing a coding interval size information describing a size of a coding interval of the arithmetic encoding before an encoding of a symbol onto a quantization level;
determine a product between the combined probability value and the quantization level.
169. The arithmetic decoder according to claim 168,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
170. The arithmetic decoder according to claim 168,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information R by Qr2(R) = (⎣R • 2-u⎦ + v ) • 2-w, where u, v and w are parameters.
171. The arithmetic decoder according to any of claims 168 to 170,
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
172. The arithmetic decoder according to any of claims 168 to 171,
wherein different value intervals of the value domain for the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
173. The arithmetic decoder according to claim 172,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the combined state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
174. The arithmetic decoder according to one of claims 146 to 173,
wherein the lookup-table defines an exponential decay.
175. The arithmetic decoder according to one of claims 146 to 174
wherein the arithmetic decoder is configured to update the plurality of variable state values according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values,
wherein A is
or deviates therefrom merely for one or more
extreme values of its argument by zero setting or magnitude reduction to avoid the updated leaving a predetermined value range,
where are predetermined parameters.

176. The arithmetic decoder according to claim 175
configured to derive by table look-up or computationally.

177. An arithmetic decoder (50; 500;1620;1720) for decoding a plurality of symbols (24”;520; 1622; 1722) having symbol values,
wherein the arithmetic decoder is configured to determine one or more state variable values ( s1k s2k; 642,644; 710;810;910;1010a,1010b;1082a,1082b;1110;
1210;1310;1410;1510;1632,1642;1732,1742), which represent statistics of a plurality of previously decoded symbol values, and
wherein the arithmetic decoder is configured to derive an interval size information (pk, R*pk) for an arithmetic decoding of one or more symbol values to be decoded on the basis of the one or more state variable values (sik), which represent statistics of a plurality of previously decoded symbol values,
wherein the arithmetic decoder is configured to update a first state variable value (sk1) in dependence on a decoded symbol and using a look-up table(A).
178. The arithmetic decoder according to claim 177,
wherein the arithmetic decoder is configured to update a second state variable value (sk2) in dependence on a decoded symbol and using the look-up table(A).
179. The arithmetic decoder according to claim 177 or claim 178,
wherein the arithmetic decoder is configured update the first state variable value and the second state variable values using different adaptation time constants.
180. The arithmetic decoder according to claim 177 or claim 178 or claim 179,
wherein the arithmetic decoder is configured to selectively increase or decrease a previous state variable value by a value determined using the look-up table in dependence on whether a decoded symbol takes a first value or a second value which is different from the first value.
181. The arithmetic decoder according to one of claims 177 to 180,
wherein the arithmetic decoder is configured to increase a previous state variable value by a comparatively larger value in case that the previous state variable value is negative when compared to a case that the previous state variable value is positive if a decoded symbol takes a first value; and
wherein the arithmetic decoder is configured to decrease a previous state variable value by a comparatively larger value in case that the previous state variable value is positive when compared to a case that the previous state variable value is negative if a decoded symbol takes a second value which is different from the first value.
182. The arithmetic decoder according to one of claims 177 to 181,
wherein the arithmetic decoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the first state variable value in dependence on a sum of a predetermined offset value (z) and a previously computed first state variable value

or a scaled and/or rounded version
thereof, if a decoded symbol takes a first value; and
wherein the arithmetic decoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the first state variable value in dependence on a sum of a predetermined offset value (z) and a in inversed version of a previously
computed first state variable value, or a scaled and/or rounded version
thereof, if a decoded symbol takes a second value.
183. The arithmetic decoder according to one of claims 177 to 182,
wherein the arithmetic decoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the second state variable value in dependence on a sum of a predetermined offset value (z) and a previously computed second state variable value or a scaled and/or rounded version thereof, if a decoded symbol

takes a first value; and
wherein the arithmetic decoder is configured to determine an index of an entry of the lookup table to be evaluated when updating the second state variable value in dependence on a sum of a predetermined offset value (z) and a in inversed version of a previously

computed second state variable value, or a scaled and/or rounded version
thereof, if a decoded symbol takes a second value.
184. The arithmetic decoder according to one of claims 177 to 183,
wherein the arithmetic decoder is configured to apply a first scaling value (mk1), to scale the previously computed first state variable value (sk1), when determining an index of an entry of the lookup table to be evaluated when updating the first state variable value, and
wherein the arithmetic decoder is configured to apply a second scaling value (mk2), to scale the previously computed second state variable value (sk2), when determining an index of an entry of the lookup table to be evaluated when updating the second state variable value, wherein the first scaling value is different from the second scaling value.
185. The arithmetic decoder according to one of claims 177 to 184,
wherein the arithmetic decoder is configured to scale a value returned by an evaluation of the lookup table using a first scaling value when updating the first state variable value,
wherein the arithmetic decoder is configured to scale a value returned by an evaluation of the lookup table using a second scaling value when updating the second state variable value,
wherein the first scaling value is different from the second scaling value.
186. The arithmetic decoder according to one of claims 177 to 185,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to

If decoded symbol is 1.
If decoded symbol is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
187. The arithmetic decoder according to one of claims 177 to 185,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to

If symbol to be encoded is 1
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
188. The arithmetic decoder according to one of claims 177 to 185,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to

If symbol to be encoded is 1,
If symbol to be encoded is 0,
wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
189. The arithmetic decoder according to one of claims 177 to 185,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to

If symbol to be encoded is 1.
If symbol to be encoded is 0.
wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
190. The arithmetic decoder according to one of claims 186 to 189,
wherein the entries of A decrease monotonically with increasing lookup table index.
191. The arithmetic decoder according to one of claims 186 to 190,
wherein A is
or deviates therefrom merely for one or more
extreme values of its argument by zero setting or magnitude reduction to avoid the updated leaving a predetermined value range,
where are predetermined parameters.
192. The arithmetic decoder according to one of claims 177 to 191,
wherein a last entry of the lookup table is equal to zero.
193. The arithmetic decoder according to one of claims 177 to 192,
wherein the arithmetic decoder is configured to apply a clipping operation to the updated state variable values, to keep the updated and clipped state variable values within a predetermined range of values.
194. The arithmetic decoder according to claim 193,
wherein the arithmetic decoder is configured to apply a clipping operation according to
to the updated state variable values,
wherein is a maximum allowed value for and
wherein is a minimum allowed value for
195. The arithmetic decoder according to one of claims 177 to 194,
wherein the arithmetic decoder is configured to apply different scaling values for different context.
196. The arithmetic decoder according to one of claims 177 to 195,
wherein the arithmetic decoder is configured to obtain the interval size information as defined in one of claims 119 to 155.
197. An arithmetic decoder (50; 500;1620;1720) for decoding a plurality of symbols (24”;520;1622;1722) having symbol values,
wherein the arithmetic decoder is configured to determine one state variable value (sk), which represent a statistic of a plurality of previously decoded symbol values, and
wherein the arithmetic decoder is configured to compute from the combined state variable value, or the scaled and/or rounded version ( [sk* ak ⎦ ) thereof, a subinterval width value (RLPS) for an arithmetic decoding of a symbol value to be decoded by
mapping the one state variable value (sk), or a scaled and/or rounded version thereof (⎣sk* ak ⎦; ⎣|sk| • ak⎦ ) using a one-dimensional look-up table (probTabLPS[Qp2(...)]) entries of which comprise probability values for different value intervals of a value domain for the combined state variable value, or the scaled and/or rounded version ( [sk* ak ⎦; ⎣|sk| • ak⎦ ) thereof, onto a combined probability value, and
quantizing a coding interval size information describing a size of a coding interval of the arithmetic encoding before the arithmetic decoding of the symbol value to be encoded onto a quantization level (Qr2(R));
determine a product between the probability value and the quantization level, wherein the arithmetic decoder is configured to perform a state variable value update in dependence on the symbol to be decoded.
198. The arithmetic decoder according to claim 197,
wherein the arithmetic decoder is configured to derive as the one state variable value (sk) a combined state variable value one the basis of a plurality of state variable values (sik) , which represent statistics of the plurality of previously decoded symbol values with different adaptation time constants.
199. The arithmetic decoder according to claim 198,
wherein the arithmetic decoder is configured to determine a weighted sum of state variable values, in order to obtain the combined state variable value.
200. The arithmetic decoder according to claim 198 or according to claim 199,
wherein the arithmetic decoder is configured to determine a sum of rounded values
which are obtained by rounding products of state variable values and

associated weight values in order to obtain the combined state variable value (sk).
201. The arithmetic decoder according to one of claims 198 to 200,
wherein the arithmetic decoder is configured to determine the combined state variable value sk according to
wherein sk2 are state variable values,
wherein N is a number of state variable values considered,
wherein ⎣ . ⎦ is a floor operator,
wherein dki are weighting values associated with the state variable values.
202. The arithmetic decoder according to one of claims 198 to 201,
wherein the arithmetic decoder is configured to, in performing the state variable value update, update the plurality of state variable values according to

If symbol to be encoded is 1.
If symbol to be encoded is 0.
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values,
wherein A is
or deviates therefrom merely for one or more
extreme values of its argument by zero setting or magnitude reduction to avoid the updated leaving a predetermined value range,
where are predetermined parameters.

203. The arithmetic decoder according to claim 202,
configured to derive by table look-up or computationally.
204. The arithmetic decoder according to one of claims 197 to 203,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.
wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
205. The arithmetic decoder according to one of claims 197 to 201,
wherein the arithmetic decoder is configured to determine one or more updated state variable values according to
If symbol to be encoded is 1,
If symbol to be encoded is 0,
wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
206. The arithmetic decoder according to one of claims 197 to 201,
wherein the arithmetic decoder is configured to determine one or more updated state variable values
according to
If symbol to be encoded is 1.
If symbol to be encoded is 0.

wherein A is a lookup table,
wherein z is a predetermined offset value;
wherein are one or more weighting values;
wherein are one or more weighting values.
207. The arithmetic decoder according to any of claims 197 to 206,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information by applying a logical right shift onto the coding interval size information.
208. The arithmetic decoder according to any of claims 197 to 206,
wherein the arithmetic decoder is configured to perform the quantizing the coding interval size information R by Qr2(R) = (⎣R • 2-u⎦ + v) • 2-w, where u, v and w are parameters.
209. The arithmetic decoder according to any of claims 197 to 208,
wherein the entries of the one-dimensional look-up table monotonically decrease at an increase of the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
210. The arithmetic decoder according to any of claims 197 to 209,
wherein different value intervals of the value domain for the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof, are equally sized.
211. The arithmetic decoder according to claim 210,
wherein the entries of the one-dimensional look-up table monotonically decrease with decreasing rate at an increase of the one state variable value, or the scaled and/or rounded version (⎣sk* ak ⎦ ) thereof.
212. A video encoder (10),
wherein the video encoder is configured to encode a plurality of video frames (12), wherein the video encoder comprises an arithmetic encoder (34;400) for providing an encoded binary sequence (420) on the basis of a sequence of binary values (410) representing a video content, according to one of claims 1 to 79 or claims 104 to 118 or claims 80 to 91.
213. A video decoder (20;1600;1700),
wherein the video decoder is configured to decode a plurality of video frames (12’),
wherein the video decoder comprises an arithmetic decoder (50;500; 1620; 1720) for providing a decoded binary sequence (24”,520;1622;1722) on the basis of an encoded representation (14;510;1610;1710) of the binary sequence, according to one of claims 119 to 196 or claim 197 to 211 or 92 to 103.
214. A method for encoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic encoding of one or more symbol values to be encoded on the basis of a plurality of state variable values (sik), which represent statistics of a plurality of previously encoded symbol values with different adaptation time constants,
wherein the method comprises mapping a first state variable value (sk1), or a scaled and/or rounded version(⎣sk1* ak1 ⎦ ) thereof, using a lookup-table (LUT1) and
mapping a second state variable value (sk2), or a scaled and/or rounded version ( ⎣sk2* ak2⎦ ) thereof using the lookup-table (LUT1),
in order to obtain the interval size information describing an interval size for the arithmetic encoding of one or more symbols to be encoded.
215. A method for encoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic encoding of one or more symbol values to be encoded on the basis of a plurality of state variable values (Sik), which represent statistics of a plurality of previously encoded symbol values (e.g. a sequence of binary values 0 and 1) with different adaptation time constants,
wherein the method comprises deriving a combined state variable value (sk) one the basis of the plurality of state variable values (sik), and
wherein the method comprises mapping the combined state variable value (sk), or a scaled and/or rounded version thereof ( ⎣sk2* ak2⎦ ) using a look-up table, in order to obtain the interval size information describing an interval size for the arithmetic encoding of one or more symbols to be encoded.
216. A method for encoding a plurality of symbols having symbol values,
wherein the method comprises determining one or more state variable values (s1k , s2k), which represent statistics of a plurality of previously encoded symbol values, and
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic encoding of one or more symbol values to be encoded on the basis of the one or more state variable values (sik), which represent statistics of a plurality of previously encoded symbol values,
wherein the method comprises updating a first state variable value (sk1) in dependence on a symbol to be encoded and using a look-up table (A).
217. A method for decoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic decoding of one or more symbol values to be decoded on the basis of a plurality of state variable values (sik), which represent statistics of a plurality of previously decoded symbol values with different adaptation time constants,
wherein the method comprises mapping a first state variable value (sk1), or a scaled and/or rounded version(⎣sk1* ak1 ⎦ ) thereof, using a lookup-table (LUT1) and
mapping a second state variable value (sk2), or a scaled and/or rounded version( ⎣sk2 * ak2⎦ ) thereof using the lookup-table (LUT1) ,
in order to obtain the interval size information describing an interval size for the arithmetic decoding of one or more symbols to be decoded.
218. A method for decoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic decoding of one or more symbol values to be decoded on the basis of a plurality of state variable values (sik), which represent statistics of a plurality of previously decoded symbol values with different adaptation time constants,
wherein the method comprises deriving a combined state variable value (sk) one the basis of the plurality of state variable values (sik), and
wherein the method comprises mapping the combined state variable value (sk), or a scaled and/or rounded version thereof ( ⎣sk2* ak2⎦ ) using a look-up table, in order to obtain the interval size information describing an interval size for the arithmetic decoding of one or more symbols to be decoded.
219. A method for decoding a plurality of symbols having symbol values
wherein the method comprises determining one or more state variable values (s1k , s2k), which represent statistics of a plurality of previously decoded symbol values, and
wherein the method comprises deriving an interval size information (pk, R*pk) for an arithmetic decoding of one or more symbol values to be decoded on the basis of the one or more state variable values (sik), which represent statistics of a plurality of previously decoded symbol values,
wherein the method comprises updating a first state variable value (sk1) in dependence on a decoded symbol and using a look-up table (A).
220 and 221. Methods performed by encoder and decoder according to claim 104 and 197, respectively.
222. A computer program for performing the method according to one of claims 214 to 221 when the computer program runs on a computer.
223. A method for encoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size value (RLPS) for an arithmetic encoding of one or more symbol values to be encoded on the basis of one or more state variable values (sik), which represent statistics of a plurality of previously encoded symbol values,
wherein the method comprises determining the interval size value (RLPS) using a base lookup table (Base TabLPS),
wherein the method comprises determining the interval size value (RLPS) such that a determined interval size value is identical to an element of the base lookup table or is a rounded version of an element of the base lookup table if a probability index (i), which is obtained on the basis of the one or more state variable values, is within a first range, and such that a determined interval size value is obtained using a scaling and rounding of an element of the base lookup table if the probability index is within a second range; and
wherein the method comprises performing the arithmetic encoding of one or more symbols using the interval size value (RLPS).
224. A method for encoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size value (RLPS) for an arithmetic encoding of one or more symbol values to be encoded on the basis of one or more state variable values (sik), which represent statistics of a plurality of previously encoded symbol values,
wherein the method comprises determining the interval size value (RLPS) using a probability table (Prob TabLPS), on the basis of a probability value derived from the one or more state variable values and on the basis of a coding interval size (R),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein the method comprises scaling an element of the probability table (Prob_TabLPS), to obtain the interval size value(RLPS) if a current probability value is not in the set of a plurality of probability values and/or if a current coding interval size (R) is different from the given coding interval size; and
wherein the method comprises performing the arithmetic encoding of one or more symbols using the interval size value (RLPS).
225. A method for decoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size value (RLPS) for an arithmetic decoding of one or more symbol values to be decoded on the basis of one or more state variable values (sik), which represent statistics of a plurality of previously decoded symbol values,
wherein the method comprises determining the interval size value (RLPS) using a base lookup table (Base TabLPS),
wherein the method comprises determining the interval size value (RLPS) such that a determined interval size value is identical to an element of the base lookup table or is a rounded version of an element of the base lookup table if a probability index (i), which is obtained on the basis of the one or more state variable values, is within a first range, and such that a determined interval size value is obtained using a scaling and rounding of an element of the base lookup table if the probability index is within a second range; and wherein the method comprises performing the arithmetic decoding of one or more symbols using the interval size value (RLPS).
226. A method for decoding a plurality of symbols having symbol values,
wherein the method comprises deriving an interval size value (RLPS) for an arithmetic decoding of one or more symbol values to be decoded on the basis of one or more state variable values (sik), which represent statistics of a plurality of previously decoded symbol values,
wherein the method comprises determining the interval size value (RLPS) using a probability table (Prob TabLPS), on the basis of a probability value derived from the one or more state variable values and on the basis of a coding interval size (R),
wherein the probability table describes interval sizes for a set of a plurality of probability values and for a given coding interval size, and
wherein the method comprises scaling an element of the probability table (Prob_TabLPS), to obtain the interval size value(RLPS) if a current probability value is not in the set of a plurality of probability values and/or if a current coding interval size (R) is different from the given coding interval size; and
wherein the method comprises performing the arithmetic decoding of one or more symbols using the interval size value (RLPS).
227. A computer program for performing the method according to one of claims 223 to 226 when the computer program runs on a computer.