Hybrid product polar codes-based communication systems and methods

A communication system comprising:

• a receiver including:
• a receiver symbol processor configured to:
• receive a set of processed non-binary symbols S′ from a transmitter, process the received set of processed non-binary symbols S′ to reverse the operations performed by a transmitter symbol processor included in the transmitter, and
• generate a set of extracted non-binary symbols S″;
• a symbols-to-log-likelihood ratio (LLR) convertor configured to convert the set of extracted non-binary symbols S″ to LLRs;
• a deinterleaver configured to rearrange the LLRs to reverse the effects of the interleaving performed by the transmitter;
• a polar decoder configured to:
• perform successive cancellation-based polar decoding over the rearranged LLRs and generate polar decoded LLRs, and
• rearrange the polar decoded LLRs to a 2D matrix of polar decoder LLRs of size Nr×Nc, where Nr is a number of rows and Nc is a number of columns;
• and
• a product polar code decoder configured to perform a product polar decoding over the 2D matrix of polar decoder LLRs to generate information bits manifesting original information bits transmitted by the transmitter.

A communication method comprising:

• receiving a stream of information bits;
• 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 where Kr1 and Kr2 are the number of rows and Kc1 and Kc2 are the number of columns in the rectangular information matrices M1 and M2 respectively;
• 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 have a size of Nr1×Nc1 and Nr2×Nc2 respectively, where Nr1 and Nr2 are number of rows and Nc1 and Nc2 are number of columns of the encoded matrices X1 and X2 respectively;
• converting the 2D product polar code encoded matrices X1 and X2 to a stream of encoded bits X′;
• encoding the stream of encoded bits X′ to a stream of polar encoded bits X″ using polar codes;
• rearranging the stream of polar encoded bits X″ to generate a stream of rearranged polar encoded bits X′″;
• mapping the stream of rearranged polar encoded bits X″ to a set of non-binary symbols S;
• processing the set of non-binary symbols S and generating a set of processed non-binary symbols S′;
• and
• transmitting the set of processed non-binary symbols S′ towards a receiver.

A communication method comprising:

• receiving a set of processed non-binary symbols S′ from a transmitter;
• processing the received set of processed non-binary symbols S′ and reversing the operations performed by a transmitter symbol processor included in the transmitter;
• generating a set of extracted non-binary symbols S″;
• converting the set of extracted non-binary symbols S″ to LLRs;
• rearranging the LLRs to reverse the effects of the interleaving performed by the transmitter;
• performing successive cancellation-based polar decoding over the rearranged LLRs and generating polar decoded LLRs;
• rearranging the polar decoded LLRs to a 2D matrix of polar decoder LLRs of size Nr×Nc, where Nr is a number of rows and Nc is a number of columns;
• and
• performing a product polar decoding over the 2D matrix of polar decoder LLRs and generating information bits manifesting original information bits transmitted by the transmitter.