Pre-coding and decoding polar codes using local feedback

A method for improving an error correction capability of an encoder, comprising:

• receiving a plurality of information symbols (k), wherein k is a positive integer;
• generating a plurality of convolutionally encoded symbols (n) by performing a convolutional encoding operation on the plurality of information symbols and a plurality of frozen symbols (n−k), wherein n is a positive integer;
• generating a plurality of polar encoded symbols by performing a polar encoding operation on the plurality of convolutionally encoded symbols, wherein the polar encoding operation is based on a transform, and wherein a rate of the polar encoding operation is one;
• and
• providing the plurality of polar encoded symbols for transmission or storage.

A method for improving an error correction capability of a decoder, comprising:

• receiving a noisy codeword vector of length n, the codeword having been generated based on a concatenation of a convolutional encoding operation and a polar encoding operation and provided to a communication channel or a storage channel prior to reception by the decoder, wherein n is a positive integer, wherein a rate of the concatenation of the convolutional encoding operation and the polar encoding operation is based on a number of frozen symbols used in the polar encoding operation;
• generating a plurality of polar decoded symbols (n) by performing a successive-cancellation decoding operation on the noisy codeword vector;
• generating a plurality of information symbols (k) by performing a convolutional decoding operation on the plurality of polar decoded symbols, wherein k is a positive integer, wherein k/n is a rate of the concatenation of the convolutional encoding operation and the polar encoding operation;
• and
• performing a bidirectional communication between the successive-cancellation decoding operation and the convolutional decoding operation.