A method for determining features of an error correcting code system, comprising independent error correcting codes and a polarization module, allowing transmitting a binary input vector on block fading sub-channels, called BF sub-channels, each BF sub-channel being affected by an Additive White Gaussian Noise with a signal to noise ratio represented by a first random variable, function of a second random variable, independent on each BF sub¬channel, representative of a fading on said BF sub-channel, and a parameter, identical on each BF sub-channel, representative of a long term signal to noise ratio on said BF sub-channel, the independent error correcting codes generating at least one component of the binary input vector and a channel polarization being applied to the binary input vector by the polarization module, to obtain a binary polarized vector, characterized in that the method comprises:
obtaining a tuple of data comprising a value of the parameter and a set, called probability distribution set, comprising, for each BF sub-channel, data representative of a probability distribution of the second random variable corresponding to said sub-channel; and,
determining features of said error correcting code system, comprising, for each error correcting code, a rate, called design rate, of said error correcting code, adapted to the obtained tuple of data and minimizing a function of a probability, called outage probability, that an instantaneous equivalent channel capacity of the BF sub-channels is below a transmission rate transmitted on the BF sub-channels, said transmission rate being the sum of the design rates, said outage probability being approximated, assuming that each component of the binary input vector is transmitted on a BF sub-channel, called polarized BF sub¬channel, of an equivalent channel created by the polarization module, by a probability, called approximated outage probability, that an instantaneous

channel capacity of at least one polarized BF sub-channel is below the design rate of the error correcting code providing the component of the binary input vector intended to be transmitted on said polarized BF sub-channel. [Claim 2]
A method according to claim 1 wherein, the polarization module is adapted to implement any polarization kernel of a predefined set of polarization kernels, and wherein, one feature of the error correcting code system determined is a polarization kernel selected in the predefined set of polarization kernels. [Claim 3]
A method according to claim 2 wherein, each polarization kernel of the predefined set of polarization kernels is a square matrix made of coefficients equal to "0" or "1", said matrix being of full rank and comprises at least one row comprising two coefficients equal to "1". [Claim 4]
A method according to anyone of claims 1, 2 or 3 wherein, when determining the features of said error correcting code system adapted to the obtained tuple of data and minimizing the function of the outage probability, a plurality of transmission rates is tested, the transmission rate maximizing a function of the outage probability representative of the throughput of the error correcting code system being selected. [Claim 5]
A method according to any previous claims wherein, the instantaneous channel capacity of a polarized BF sub-channel is computed as a mutual information between the component, called current component, intended to be transmitted on said polarized sub-channel and an output vector resulting from the transmission of the binary polarized vector on the BF sub-channels, knowing each component of the binary input vector with which the current component interferes after channel polarization by the polarization module and a set of first

random variables comprising the first random variables of each BF sub-channel; and,
the features minimizing the outage probability are determined using a statistical method comprising:
evaluating an instantaneous channel capacity for each polarized BF sub¬channel, for each set of first random variables of a plurality of possible sets of first random variables and for each polarization kernel of the predefined set of polarization kernels; and,
for each value of the parameter comprised in a pre-defined set of values of the parameter, for each probability distribution set of a pre-defined plurality of probability distribution sets and for each transmission rate of a pre-defined set of transmission rates using the evaluated instantaneous channel capacities to determine the features of said error correcting code system minimizing the approximated outage probability for said value of the parameter, said probability distribution set and said transmission rate.. [Claim 6]
A method according to claim 5 wherein the instantaneous channel capacity of each polarized BF sub-channel is evaluated for one set of first random variables of the plurality of possible sets of first random variables and one polarization kernel of the predefined set of polarization kernels by using a process based on a Monte-Carlo simulation and a belief propagation decoding on said one polarization kernel with a genie-aided method that assumes perfect a priori input for the components of the binary input vector with which the component intended to be transmitted on said sub-channel interferes after channel polarization by the polarization module, said process comprising for each polarized BF sub-channel:
iteratively generating a random Log Likelihood Ratio L following a Gaussian distribution and performing a belief propagation decoding of said

random Log Likelihood Ratio L on said polarization kernel and computing a value representative of an estimation J' of the instantaneous channel capacity of said polarized BF sub-channel using a result L' of the belief propagation decoding of the random Log Likelihood Ratio L as follows:
J'= 1 - log2(l + expi-L'));
and,
evaluating the instantaneous channel capacity of said polarized BF sub¬channel as an average of the estimations 7' of the instantaneous channel capacity of said polarized BF sub-channel. [Claim 7]
A method according to claim 5 or 6 wherein when determining the features of said error correcting code system minimizing the approximated outage probability for each value of the parameter comprised in the pre-defined set of values of the parameter, for each probability distribution set of the pre-defined plurality of probability distribution sets and for each transmission rate of the pre¬defined set of transmission rates, an approximated outage probability is computed for each polarization kernel of the predefined set of polarization kernels and for each set of design rates of a plurality of sets of design rates, each set of design rates of said plurality of sets of design rates comprising a design rate for each error correcting code. [Claim 8]
A method according to claim 7 wherein each approximated outage probability is obtained for a value of the parameter, for a probability distribution set and for a design rate by a numerical integration of a product of probability density functions of the first random variables on a region such that the instantaneous channel capacity of at least one polarized BF sub-channel is below the design rate of the error correcting code providing the component of the binary input vector intended to be transmitted on said polarized BF sub-channel,

the probability density functions of the first random variable being determined using said value of the parameter and said probability distribution set. [Claim 9]
A method according to claim 7 wherein the approximated outage probability is obtained by a Monte-Carlo simulation that generates random realizations of the first random variables and accumulates an error event if the instantaneous channel capacity of at least one polarized BF sub-channel is below the design rate of the error correcting code providing the component of the binary input vector intended to be transmitted on said polarized BF sub-channel. [Claim 10]
A method according to any claim from claim 5 to claim 9, wherein the statistical method is implemented offline and allows obtaining a table, called correspondence table, comprising, for each value of the parameter comprised in the pre-defined set of values of the parameter and for each probability distribution set of the pre-defined plurality of probability distribution sets the features of the error correcting code system adapted to said value of the parameter and said probability distribution set and minimizing the outage probability, the features of the error correcting code system adapted to the obtained tuple of data and minimizing the outage probability being determined by using said correspondence table. [Claim 11]
A device for determining features of an error correcting code system, comprising independent error correcting codes and a polarization module, allowing transmitting a binary input vector on block fading sub-channels, called BF sub-channels, each BF sub-channel being affected by an Additive White Gaussian Noise with a signal to noise ratio represented by a first random variable, function of a second random variable, independent on each BF sub¬channel, representative of a fading on said BF sub-channel, and a parameter,

identical on each BF sub-channel, representative of a long term signal to noise ratio on said BF sub-channel, the independent error correcting codes generating at least one component of the binary input vector and a channel polarization being applied to the binary input vector by the polarization module, to obtain a binary polarized vector, characterized in that the device comprises:
obtaining means for obtaining a tuple of data comprising a value of the parameter and a set, called probability distribution set, comprising, for each BF sub-channel, data representative of a probability distribution of the second random variable corresponding to said BF sub-channel; and,
determination means for determining features of said error correcting code system, comprising, for each error correcting code, a rate, called design rate, of said error correcting code, adapted to the obtained tuple of data and minimizing a probability, called outage probability, that an instantaneous equivalent channel capacity of the BF sub-channels is below a transmission rate transmitted on the BF sub-channels, said transmission rate being the sum of the design rates, said outage probability being approximated, assuming that each component of the binary input vector is transmitted on a BF sub-channel, called polarized BF sub¬channel, of an equivalent channel created by the polarization module, by a probability, called approximated outage probability, that an instantaneous channel capacity of at least one polarized BF sub-channel is below the design rate of the error correcting code providing the component of the binary input vector intended to be transmitted on said polarized BF sub-channel. [Claim 12]
A method for transmitting each component of a binary input vector on a different block fading sub-channel, called BF sub-channel, of a plurality of BF sub-channels, each BF sub-channel of said plurality being affected by an Additive White Gaussian Noise with a signal to noise ratio represented by a first random variable, function of a second random variable, independent on each BF

sub-channel, representative of a fading on said BF sub-channel, and a parameter, identical on each BF sub-channel, representative of a long term signal to noise ratio on said BF sub-channel, independent error correcting codes generating at least one component of the binary input vector and a channel polarization being applied to the binary input vector by a polarization module to obtain a binary polarized vector, the independent error correcting codes and the polarization module being comprised in an error correcting code system characterized in that the method comprises:
applying the method according to any claim from claim 1 to claim 10 for determining features of the error correcting code system;
generating the binary polarized vector using the features of the error correcting code system determined; and,
providing said binary polarized vector to a modulation module insuring a modulation of said binary polarized vector before its transmission. [Claim 13]
A transmission system comprising an error correcting code system allowing transmitting a binary input vector on block fading sub-channels, called BF sub-channels, each BF sub-channel being affected by an Additive White Gaussian Noise with a signal to noise ratio represented by a first random variable, function of a second random variable, independent on each BF sub¬channel, representative of a fading on said BF sub-channel, and a parameter, identical on each BF sub-channel, representative of a long term signal to noise ratio on said BF sub-channel, the error correcting code system comprising independent error correcting codes, each adapted to generate at least one component of the binary input vector, and a polarization module, adapted to apply a channel polarization to the binary input vector to obtain a binary polarized vector, the transmission system being characterized in that it comprises a device according to claim 11.

[Claim 14]
A receiver system comprising an inverse error correcting code system adapted to decode an output vector resulting from a transmission, by a transmission system, of a binary polarized vector on block fading sub-channels, called BF sub-channels, each BF sub-channel being affected by an Additive White Gaussian Noise with a signal to noise ratio represented by a first random variable function of a second random variable, independent on each BF sub¬channel, representative of a fading on said BF sub-channel, and a parameter, identical on each BF sub-channel, representative of a long term signal to noise ratio on said BF sub-channel, the binary polarized vector having been generated by an error correcting code system comprised in the transmission system comprising independent error correcting codes each adapted to generate at least one component of a binary input vector and, a polarization module adapted to apply a channel polarization to the binary input vector to obtain the binary polarized vector, the receiver system being characterized in that it comprises a device according to claim 11 allowing determining features of the error correcting code system and means for transmitting the determined features to the transmission system. [Claim 15]
A computer program comprising program code instructions which can be loaded in a programmable device for implementing the method according to any previous claim from claim 1 to 10, when the program code instructions are run by the programmable device. [Claim 16]
Information storage means storing a computer program comprising program code instructions which can be loaded in a programmable device for implementing the method according to any previous claim from claim 1 to 10, when the program code instructions are run by the programmable device.