Decoding Reed-Muller Codes with Successive Codeword Permutations

A novel recursive list decoding (RLD) algorithm of Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. An SP scheme that performs maximum likelihood decoding on a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is applied to an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, an efficient latency reduction scheme is introduced that virtually preserves the error-correction performance of the proposed decoder. Simulation results demonstrate that for the RM code of size $256$ with $163$ information bits, the proposed decoder reduces $39\%$ of the computational complexity, $36\%$ of the decoding latency, and $74\%$ of the memory requirement of the state-of-the-art RLD algorithm with list size $64$ that also uses the permutations from the full symmetry group of RM codes, while only incurring an error-correction performance degradation of $0.1$ dB at the target frame error rate of $10^{-3}$.