Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong diversity gains, however, requires constructing many subcodes that satisfy a linear covering property-yet existing approaches lack a systematic way to scale the ensemble size while preserving this property. This paper introduces hierarchical subcode ensemble decoding (HSCED), a new ensemble decoding framework that expands the number of constituent decoders while still guaranteeing linear covering. The key idea is to recursively generate subcode parity constraints in a hierarchical structure so that coverage is maintained at every level, enabling large ensembles with controlled complexity. To demonstrate its effectiveness, we apply HSCED to belief propagation (BP) decoding of polar codes, where dense parity-check matrices induce severe stopping-set effects that limit conventional BP. Simulations confirm that HSCED delivers significant block-error-rate improvements over standard BP and conventional subcode-ensemble decoding under the same decoding-latency constraint.

翻译：子码集成译码器通过在多组精心选取的子码上并行运行多个译码器，增加至少一个译码器避开主要陷阱结构的可能性，从而改进迭代译码性能。然而，要实现显著的多样性增益，需要构造大量满足线性覆盖性质的子码——而现有方法缺乏在保持该性质的同时系统性地扩展集成规模的途径。本文提出了层次化子码集成译码（HSCED），这是一种新的集成译码框架，能够在保证线性覆盖的前提下扩展组成译码器的数量。其核心思想是在层次化结构中递归地生成子码奇偶校验约束，使得每一层级都保持覆盖性，从而实现复杂度可控的大规模集成。为验证其有效性，我们将HSCED应用于极化码的置信传播（BP）译码，其中密集的奇偶校验矩阵会引发严重的停止集效应，从而限制传统BP译码的性能。仿真结果表明，在相同译码延迟约束下，HSCED相较于标准BP译码和传统子码集成译码，能带来显著的块错误率性能提升。