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.

翻译：循环解码列表的版本已知用于处理短长度 Reed- Muller (RM) 代码的最大相似性(ML)性能。 循环解码器使用Plotkin 构造将原代码分成两个较短的 RM 代码, 首先对较低级 RM 代码进行解码。 在本文中, 我们考虑 RM 代码的无线软输入解码器, 与循环解码不同, 开始用高利率组成代码解码。 虽然这些算法的错误率性能有限, 但通过应用该代码自定义组的变换, 它可以大大改进, 将原始代码分为两个较短的 RM 代码。 模拟结果显示, 以调色选择技术增强的拟议算法的错误率性能接近基于自定义的再现解码, 与短长度的( leq 256) $ RM 代码相近, 而我们的解码在接近的RM RM 3 代码上表现得更好。 具体来说, 以 RM 3 的复杂性 。