With the increasing demands on future wireless systems, new design objectives become eminent. Low-density parity-check codes together with belief propagation (BP) decoding have outstanding performance for large block lengths. Yet, for future wireless systems, good decoding performance for short block lengths is mandatory, a regime in which BP decoding typically shows a significant gap to maximum likelihood decoding. Automorphism ensemble decoding (AED) is known to reduce this gap effectively and, in addition, enables an easy trade-off between latency, throughput, and complexity. Recently, generalized AED (GAED) was proposed to increase the set of feasible automorphisms suitable for ensemble decoding. By construction, GAED requires a preprocessing step within its constituent paths that results in information loss and potentially limits the gains of GAED. In this work, we show that the preprocessing step can be merged with the Tanner graph of BP decoding, thereby improving the performance of the constituent paths. Finally, we show that the improvement of the individual paths also enhances the overall performance of the ensemble.

翻译：随着对未来无线系统需求的日益增长，新的设计目标变得突出。低密度奇偶校验码与置信传播解码在大码长下具有出色的性能。然而，对于未来的无线系统，短码长下的良好解码性能是必需的，而在此区间内，BP解码通常与最大似然解码存在显著差距。已知自同构集成解码能有效缩小这一差距，并且还能在延迟、吞吐量和复杂度之间实现灵活的权衡。最近，广义自同构集成解码被提出，以扩大适用于集成解码的可行自同构集合。通过构造，GAED在其组成路径中需要一个预处理步骤，这会导致信息损失，并可能限制GAED的增益。在这项工作中，我们表明预处理步骤可以与BP解码的Tanner图合并，从而提高组成路径的性能。最后，我们证明单个路径的改进也能提升集成解码的整体性能。