Polar Code Constructions Based on LLR Evolution

Polar code constructions based on mutual information or Bhattacharyya parameters of bit-channels are intended for hard-output successive cancellation (SC) decoders, and thus might not be well designed for use with other decoders, such as soft-output belief propagation (BP) decoders or successive cancellation list (SCL) decoders. In this letter, we use the evolution of messages, i.e., log-likelihood ratios, of unfrozen bits during iterative BP decoding of polar codes to identify weak bit-channels, and then modify the conventional polar code construction by swapping these bit-channels with strong frozen bit-channels. The modified codes show improved performance not only under BP decoding, but also under SCL decoding. The code modification is shown to reduce the number of low-weight codewords, with and without CRC concatenation.