Device, system and method for efficient coset decoder by transform

A device comprising:

• one or more memories to store a noisy version of an error correction codeword;
• and
• one or more processors to:
• transform, from an initial domain to a transformed domain, one or more symbol probabilities that one or more individual symbols of the received error correction codeword were transmitted as one or more symbols in candidate transmitted error correction codewords;
• in the transformed domain, compose a plurality of the transformed symbol probabilities to generate a combined coset probability defining the likelihood that the transmitted error correction codeword is associated with the individual symbols belongs to a particular one of a plurality of candidate cosets, wherein the plurality of candidate cosets are mutually exclusive subsets of a codebook defining all possible values of the error correction codeword,
• inverse transform, from the transformed domain to the initial domain, a plurality of the coset probabilities for the plurality of respective cosets.

A non-transitory computer readable medium comprising instructions which when implemented on one or more processors in a maximum likelihood coset decoder cause the decoder to:

• receive a noisy version of an error correction codeword;
• transform, from an initial domain to a transformed domain, one or more symbol probabilities that one or more individual symbols of the received error correction codeword were transmitted as one or more symbols in candidate transmitted error correction codewords;
• in the transformed domain, compose a plurality of the transformed symbol probabilities to generate a combined coset probability defining the likelihood that the transmitted error correction codeword is associated with the individual symbols belongs to a particular one of a plurality of candidate cosets, wherein the plurality of candidate cosets are mutually exclusive subsets of a codebook defining all possible values of the error correction codeword;
• and
• inverse transform, from the transformed domain to the initial domain, a plurality of the coset probabilities for the plurality of respective cosets.