Systems and methods for using not perfectly polarized bit channels in parallel polar codes

An encoder that encodes information bits for transmission across a communication channel, the encoder comprising at least one processor and a memory storing programmed instructions that, when executed by the at least one processor, cause the encoder to perform the following steps:

• distributing the information bits between m parallel polar codes such that each of the m parallel polar codes includes a subset of the information bits, wherein m is the number of parallel polar codes;
• splitting the subset of information bits in each of the m parallel polar codes into a protected information section and a full rate information section, information bits in the protected information section of each of the m parallel polar codes being arranged in positions in a plurality of first bit channels in the respective parallel polar code of the m parallel polar codes and grouped into a plurality of L blocks, wherein each of the plurality of L blocks comprises a subset of the information bits in the protected information section, wherein L is the number of blocks;
• protecting the information bits in the protected information section of each of the m parallel polar codes;
• arranging a plurality of frozen bits in each of the m parallel polar codes, with the plurality of frozen bits being arranged in positions in a plurality of second bit channels that have a capacity near zero;
• and
• generating a polar encoded codeword for each of the m parallel polar codes.

A decoder comprising:

• at least one processor and a memory storing programmed instructions that, when executed by the at least one processor, cause the decoder to perform the following steps:
• receiving m polar coded codewords over a communication channel, each of the m polar coded codewords encoding a subset of information bits in a plurality of nodes and a frozen bit, wherein the information bits are distributed between the m polar coded codewords and m is the number of polar coded codewords;
• and
• for each of the m polar coded codewords, decoding the polar coded codeword to generate a decoded message comprising a decoded bit for the frozen bit, a first part for a node in a full rate information section of the polar coded codeword and a second part for a node in a full rate information section of the polar coded codeword, wherein the decoded bit is generated based on a predetermined value, the first part is generated based on a log-likelihood ratio (LLR) decoding algorithm and the second part is generated based on an averaged LLR decoding algorithm.