Abstract: The disclosed hybrid product polar codes-based communication systems and methods for i) receiving a stream of information bits; ii) reshaping the stream of information bits into at least a first rectangular information matrix M1 of size Kr1×Kc1 and a second rectangular information matrix M2 of size Kr2×Kc2; iii) converting the rectangular information matrices M1 and M2 to 2D product polar code encoded matrices X1 and X2 respectively using product polar codes, the 2D product polar code encoded matrices X1 and X2 having a size of Nr1×Nc1 and Nr2×Nc2 respectively; iv) converting the 2D product polar code encoded matrices X1 and X2 to a stream of encoded bits X?; and v) encoding the stream of encoded bits X? to a stream of polar encoded bits X? using the polar codes.

Abstract: A polar encoder comprises an input, an output and a processor operatively connected to the input and to the output. The input either receives first, second and third codewords, or receives information bits used by the processor for generating first, second and third probabilistic constellation shaping codewords. The processor combines the first and second codewords, to produce a first modulation symbol bit, combines the first and third codewords to produce a second modulation symbol bit, and combines the first, second and third codewords to produce a third modulation symbol bit. The output forwards the modulation symbol bits to a bit to symbol mapper. The polar encoder may be included in a transmitter that further comprises the bit to symbol mapper receiving the modulation symbol bits and generating modulation symbols, and a modulator modulating a carrier using the modulation symbols.

Abstract: A polar encoder comprises an input, an output and a processor operatively connected to the input and to the output. The input either receives first, second and third codewords, or receives information bits used by the processor for generating first, second and third probabilistic constellation shaping codewords. The processor combines the first and second codewords, to produce a first modulation symbol bit, combines the first and third codewords to produce a second modulation symbol bit, and combines the first, second and third codewords to produce a third modulation symbol bit. The output forwards the modulation symbol bits to a bit to symbol mapper. The polar encoder may be included in a transmitter that further comprises the bit to symbol mapper receiving the modulation symbol bits and generating modulation symbols, and a modulator modulating a carrier using the modulation symbols.

Abstract: The disclosed systems and methods for encoding, by a polar encoder, K message bits into an encoded message bits sequence C(M) using polar codes, where K and M are integer values and M is greater than or equal to K; rearranging, by an interleaver, the encoded message bits sequence C(M) to 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 ; mapping, by a bits-to-symbol mapper, the rearranged encoded message bits sequence C(M) to N non-binary symbols, where N is an integer value; and processing, by a transmitter symbol processor, the N non-binary symbols to transmit the processed non-binary symbols towards a receiver.