This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

中文翻译：

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重新审视有序统计解码：距离分布和解码规则


本文重新审视了有序统计解码（OSD）。它通过表征 OSD 算法再处理阶段从码字估计到接收序列的汉明距离和加权汉明距离的统计特性、演化和分布，对 OSD 算法进行全面分析。我们证明汉明距离和加权汉明距离分布可以表征为捕获解码错误概率和代码权重枚举器的混合模型。模拟和数值结果表明，我们提出的统计方法可以准确地描述距离分布。基于这些分布，以降低解码复杂度为目标，提出了包括停止规则和丢弃规则在内的几种技术，并相应地分析了它们的解码错误性能和复杂度。解码各种 eBCH 代码的仿真结果表明，所提出的技术可以显着降低解码复杂度，而解码错误性能的损失可以忽略不计。