Method and device for determining features of error correcting code system

A device for determining a transmission rate of an error correcting code system which improves throughput, comprising independent error correcting codes and transmitting a binary input vector on block fading (BF) sub-channels, each BF sub-channel being affected by an Additive White Gaussian Noise with a signal to noise ratio independently represented on each BF sub-channel by a corresponding first random fading variable, and a probability density function representative of a probability distribution of the first random fading variable representative of a fading on a respective BF sub-channel, and a long term SNR parameter, identical on each BF sub-channel, representative of a long term signal to noise ratio on said respective BF sub-channels, the independent error correcting codes generating at least one component of the binary input vector and a channel polarization applied to the binary input vector to obtain a binary polarized vector, the device comprising:

• a polarization module that applied the channel polarization to the binary input vector;
• a modulation module that transmits the binary input vector on the BF sub-channels;
• and
• a processing module configured to
• obtain a tuple of data including a value of the long term SNR parameter and a probability distribution set, the probability distribution set including, for each BF sub-channel, data representative of a probability density function distribution of the probability distribution of the first random fading variable corresponding to a corresponding BF sub-channel;
• determine an optimized transmission rate for system throughput based on the long term SNR of said error correcting code system by
• obtaining a set of design rates leading to an average transmission rate, the set of design rates includes, for each error correcting code, a design rate associated with the combination of parameter values included in the obtained tuple of data,
• approximating an outage probability representing the probability that an instantaneous channel capacity of at least one polarized BF sub-channel is below the obtained design rate of the error correcting code based on the assumption that each component of the binary input vector is transmitted on a polarized BF sub-channel of an equivalent channel created by the polarization module, and
• obtaining a kernel associated with the long term SNR parameter value included in the obtained tuple of data and minimizing the approximated outage probability for the average transmission rate,
• generating binary polarized vectors using the determined optimized transmission rate and providing the binary polarized vectors to the modulation module, and
• providing the generated polarized vectors to the modulation module and transmitting the modulated binary polarized vectors, wherein
• said optimized transmission rate is the sum of the design rates.