This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with information-theoretically grounded flipping rules. In particular, we reinterpret stochastic Chase decoding as a random-coding construction for error-pattern covering codes. Our approach builds on the framework of Nguyen et al., who introduced a rate-distortion formulation of multiple-attempt decoding for Reed-Solomon codes over nonbinary channels. In their formulation, erasure patterns are generated so as to align with, and thereby mask, hard-decision errors. We adapt this framework to the design of bit-flip probabilities for Chase decoding over BMS channels. This yields an explicit characterization of the asymptotically optimal bit-flipping rule, together with the expected list size required to ensure that the transmitted codeword appears in the decoding list with high probability. Moreover, for binary and quaternary symmetric channels, we demonstrate that the optimal bit-flipping rule, determined by exhaustive search, closely matches the information-theoretic rule even at short block lengths.

翻译：本文针对二进制无记忆对称（BMS）信道上的代数码，提出了一种基于率失真的随机Chase译码方法，用信息论意义上的翻转规则替代了传统上用于确定翻转概率的启发式方法。具体而言，我们将随机Chase译码重新解释为错误模式覆盖码的随机编码构造。该方法建立在Nguyen等人的框架之上，他们针对非二进制信道上的Reed-Solomon码提出了多尝试译码的率失真表述。在该表述中，擦除模式的生成旨在对齐并掩盖硬判决错误。我们将该框架应用于BMS信道上Chase译码的比特翻转概率设计。由此，我们得到了渐近最优比特翻转规则的显式刻画，以及确保发送码字以高概率出现在译码列表中所需的预期列表大小。此外，对于二进制和四进制对称信道，我们通过穷举搜索确定的最优比特翻转规则，即使在短码长下也与信息论规则高度吻合。