Automorphism-based polar encoding and decoding

A decoding apparatus, comprising:

• a data storage comprising processor-executable instructions;
• and
• at least one processor coupled to the data storage and configured, based on executing the processor-executable instructions, to facilitate the following being performed by the decoding apparatus:
• receiving a codeword from a communication channel, wherein the received codeword comprises a linear combination of information bits of an information word and frozen bits of a polar code, wherein the frozen bits are configured to support a predefined set of automorphisms that provides a mapping of the received codeword of the polar code to at least one other codeword of the polar code, and wherein the predefined set of automorphisms is based on a binary upper triangular matrix having a diagonal including at least one of zeros and units;
• obtaining a plurality of permuted versions of the received codeword by applying the predefined set of automorphisms to the received codeword;
• obtaining a plurality of candidate codewords by decoding each of the permuted versions of the received codeword;
• and
• selecting a candidate codeword from the obtained plurality of candidate codewords.

An encoding method, comprising:

• receiving, by an encoding apparatus, an information word comprising information bits;
• generating, by the encoding apparatus, a codeword by applying a polar code to the information word, wherein the codeword comprises a linear combination of the information bits and frozen bits of the polar code, wherein the frozen bits are configured to support a predefined set of automorphisms that provides a mapping of the codeword of the polar code to at least one other codeword of the polar code, and wherein the predefined set of automorphisms is based on a binary upper triangular matrix having a diagonal including at least one of zeros or units;
• and
• sending, by the encoding apparatus, the codeword over a communication channel.