Joint Design of Permutations and Polar Code Under BPL Decoding

Recently, belief propagation list (BPL) decoding of polar codes has been proposed for achieving state-of-the-art performance. By representing a polar code factor graph permutation with an equivalent bit index permutation, a single decoder can be applied on different permutated factor graphs, which is hardware-friendly. Nevertheless, the design of permutations under BPL decoding turns out to be cumbersome and highly relevant with the code structure. In this work, we propose a two-step approach for the joint design of permutations and polar code under BPL decoding. Firstly, an empirical approach is proposed for selection of good initial permutations under BPL decoding. Then, the joint optimization of permutations and polar code is implemented based on genetic algorithm. With the aid of an outer cyclic redundancy check (CRC) code, the proposed BPL scheme is shown to perform very close to CRC aided successive cancellation list (CA-SCL) decoding at practical SNRs.