Systems and methods for encoding digital communications

A communication system comprising:

• a transmitter including:
• a polar encoder configured to encode K message bits u(K) into an encoded message bits sequence C(M) using polar codes, where K is an integer value, M is an even integer value and M is greater than or equal to K;
• an interleaver configured to rearrange the encoded message bits sequence C(M) to generate rearranged encoded message bits sequence C′(M) such that a C(i)th bit and a
• C
• ⁡
• (
• M
• 2
• +
• i
• )
• th bit of the encoded message bits sequence C(M) are arranged together, where i is an integer value that varies between 1 to
• M
• 2
• ;
• a bits-to-symbol mapper configured to map the rearranged encoded message bits sequence C′(M) to N non-binary symbols, where N is an integer value;
• a transmitter symbol processor configured to process the N non-binary symbols to transmit the N processed non-binary symbols towards a receiver;
• and
• wherein:
• at least some of bit channels associated with the polar encoder are frozen bit channels and remaining bit channels are information bit channels,
• the frozen bit channels and the information bit channels are selected based on a selection process,
• the selection process includes operating the communication system in offline mode, and
• selecting M offline codewords as output of the polar encoder, such that when the M offline codewords are converted to N offline non-binary symbols, by the bits-to-symbol mapper, an average power of the N offline non-binary symbols is equal to an average power of the N available non-binary symbols with the bits-to-symbol mapper.