Recursive Decoding of Reed-Muller Codes Starting With the Higher-Rate Constituent Code

Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximumlikelihood (ML) performance of short length (<= 256) RM codes. Recursive decoding employs the Plotkin construction to split the original code into two shorter RM codes with different rates. In contrast to the standard approach which decodes the lower-rate code first, the method in this paper decodes the higher-rate code first. This modification enables an efficient permutation-based decoding technique, with permutations being selected on the fly from the automorphism group of the code using soft information from a channel. Simulation results show that the error-rate performance of the proposed algorithms, enhanced by a permutation selection technique, is close to that of the automorphism-based recursive decoding algorithm with similar complexity for short RM codes, while our decoders perform better for longer RM codes. In particular, it is demonstrated that the proposed algorithms achieve near-ML performance for short RM codes and for RM codes of length 2(m) and order m - 3 with reasonable complexity.

Automated summary

This paper introduces a recursive list decoding method for Reed-Muller (RM) codes, which splits the original code into two shorter RM codes with different rates using the Plotkin construction. By decoding the higher-rate code first, an efficient permutation-based decoding technique is enabled, with permutations selected from the automorphism group of the code using soft information from a channel. Simulation results show that the proposed algorithms achieve error-rate performance close to that of the automorphism-based recursive decoding algorithm, with better performance for longer RM codes.