High-throughput decoding of BCH codes necessitates efficient and parallelizable decoders. However, the algebraic rigidity of BCH codes poses significant challenges to applying parallel belief propagation variants. To address this, we propose a systematic design scheme for constructing parity-check matrices using a heuristic approach. This involves a sequence of binary sum operations and row cyclic shifts on the standard parity-check matrix, aiming to generate a redundant, low-density, and quasi-regular matrix with significantly fewer length-4 cycles. The relationships between frame error rate, rank deficiency of minimum-weight dual-code codewords, and row redundancy are empirically analyzed. For the revised normalized min-sum decoder, we introduce three types of random automorphisms applied to decoder inputs. These are unpacked and aggregated by summing messages after each iteration, achieving a 1-2dB improvement in bit error rate compared to parallelizable counterparts and two orders of magnitude faster convergence in iterations than iterative rivals. Additionally, undetected errors are highlighted as a non-negligible issue for very short BCH codes.

翻译：BCH码的高吞吐量解码需要高效且可并行化的解码器。然而，BCH码的代数刚性对应用并行置信传播变体构成了重大挑战。为解决此问题，我们提出了一种使用启发式方法构建奇偶校验矩阵的系统化设计方案。该方法涉及对标准奇偶校验矩阵进行一系列二进制求和运算和行循环移位，旨在生成一个冗余、低密度、准正则且显著减少长度为4环路的矩阵。我们通过实验分析了帧错误率、最小权重对偶码码字的秩亏缺以及行冗余之间的关系。对于改进的归一化最小和解码器，我们引入了三种应用于解码器输入的随机自同构。这些自同构在每次迭代后通过求和消息进行解包和聚合，与可并行化的同类解码器相比，实现了1-2dB的误码率提升，并且迭代收敛速度比迭代式竞争对手快两个数量级。此外，对于极短的BCH码，未检测错误被强调为一个不可忽视的问题。