In the short block length regime, ensemble decoding schemes with their inherently parallel structure can improve error correction performance and reduce latency compared to stand-alone suboptimal decoders such as belief propagation (BP). In this work, we introduce affine subcode ensemble decoding (aSCED), which uses an ensemble of decoders operating on linear block codes and both linear and strictly affine subcodes. This generalizes the recently proposed subcode ensemble decoding (SCED), which is restricted to linear subcodes. We derive BP update rules for affine subcodes and show that aSCED simplifies ensemble design compared to SCED, multiple bases BP, and automorphism ensemble decoding. Monte-Carlo simulations of two low-density parity-check codes and two Bose-Chaudhuri-Hocquenghem (BCH) codes demonstrate improved error correction performance of aSCED over competing existing ensemble schemes. Notably, for one BCH code, when combining ensemble design with algorithms for constructing high-performance parity-check matrices, aSCED achieves near-maximum likelihood performance using only 64 BP decoding paths.

翻译：在短分组长度范围内，具有固有并行结构的系综译码方案相较于独立次优译码器（如置信传播）可提升纠错性能并降低延迟。本文提出仿射子码系综译码，该方案采用作用于线性分组码及其线性与严格仿射子码的译码器系综，推广了近期提出的仅适用于线性子码的子码系综译码。我们推导了仿射子码的置信传播更新规则，并证明仿射子码系综译码相较于子码系综译码、多基置信传播及自同构系综译码简化了系综设计。针对两个低密度奇偶校验码和两个Bose-Chaudhuri-Hocquenghem码的蒙特卡洛仿真表明，仿射子码系综译码在纠错性能上优于现有竞争性系综方案。值得注意的是，对于某个BCH码，当将系综设计与高性能校验矩阵构建算法相结合时，仿射子码系综译码仅需64条置信传播译码路径即可实现接近最大似然的性能。