CS-FSCL decoding algorithm of polar codes based on critical sets

In order to reduce the number of redundant candidate codewords generated by the fast successive cancellation list (FSCL) decoding algorithm for polar codes, a simplified FSCL decoding algorithm based on critical sets (CS-FSCL) of polar codes is proposed. The algorithm utilizes the number of information bits belonging to the CS in the special nodes, such as Rate-1 node, repetition (REP) node and single-parity-check (SPC) node, to constrain the number of the path splitting and avoid the generation of unnecessary candidate codewords, and thus the latency and computational complexity are reduced. Besides, the algorithm only flips the bits corresponding to the smaller log-likelihood ratio (LLR) values to generate the sub-maximum likelihood (sub-ML) decoding codewords and ensure the decoding performance. Simulation results show that for polar codes with the code length of 1 024, the code rates of 1/4, 1/2 and 3/4, the proposed CS-FSCL algorithm, compared with the conventional FSCL decoding algorithm, can achieve the same decoding performance, but reduce the latency and computational complexity at different list sizes. Specifically, under the list size of L=8, the code rates of R=1/2 and R=1/4, the latency is reduced by 33% and 13% and the computational complexity is reduced by 55% and 50%, respectively.