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

List versions of recursive decoding are known to approach maximum-likelihood (ML) performance for the short length Reed-Muller (RM) codes. The recursive decoder employs the Plotkin construction to split the original code into two shorter RM codes, with a lower-rate RM code being decoded first. In this paper, we consider non-iterative soft-input decoders for RM codes that, unlike recursive decoding, start decoding with a higher-rate constituent code. Although the error-rate performance of these algorithms is limited, it can be significantly improved by applying permutations from the automorphism group of the code, with permutations being selected on the fly based on 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 length $(\leq 256)$ 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 RM codes of length $2^m$ and order $m - 3$ with reasonable complexity.