Method and system for error correction in transmitting data using low complexity systematic encoder

A systematic polar encoder with data checks, comprising:

• a data mapper configured to receive an input data word d containing information to be polar coded for transmission and generate a modified data word d′;
• a nonsystematic polar encoder configured to receive the modified data word d′ and generate a transform output z for a codeword x, the nonsystematic polar encoder implementing a transform matrix G that encodes the modified data word d′ to produce the transform output z for the codeword x such that, for some sub-sequence of coordinates S, xS=d,
• wherein the transform matrix G is constrained by an input partition (F,C,I,T), where |C|>0, and an output partition (P,J,R) so that GI,P=0, GC,P=0, GF,P=0, and GT,P is invertible;
• and
• a transceiver configured to transmit the codeword x.

A method, comprising:

• receiving an input data word d containing information to be polar coded for transmission at a data mapper;
• generating a modified data word d′ using the data mapper;
• receiving the modified data word d′ at a nonsystematic polar encoder;
• generating, using the nonsystematic polar encoder, a transform output z for a codeword x by a transform matrix G that encodes the modified data word d′ to produce the transform output z for the codeword x such that, for some sub-sequence of coordinates S, xS=d, wherein the transform matrix G is constrained by an input partition (F,C,I,T), where |C|>0, and an output partition (P,J,R) so that GI,P=0, GC,P=0, GF,P=0, and GT,P is invertible;
• and
• transmitting the codeword x using a transceiver.