In the pursuit of designing highly effective decoders for short LDPC codes nearing maximum likelihood performance, we employ a relayed decoding strategy. A neural min-sum decoder initiates the decoding process, and its errors undergo postprocessing through an adaptive ordered statistics decoding. Several key initiatives supporting the latter are emphasized. Firstly, soft information at each iteration of the neural min-sum decoder is gathered and input into a convolutional neural network to enhance bit reliability estimates. This process identifies error-prone bits, either excluding them from the most reliable basis or concentrating them at the forefront, both advantageous for the adaptive ordered statistical decoding. Additionally, a decoding path, comprising a list of order patterns, directs the postprocessing process. Adjustable path length and refined constraints on associated order patterns offer diverse means of complexity management. Simultaneously, a novel auxiliary criterion is introduced to significantly reduce the list size of codeword candidates in the adaptive ordered statistics decoding. Extensive experimental results and complexity analysis validate the serial architecture, equipped with these innovations, as a formidable contender against state-of-the-art decoders for short LDPC codes.

翻译：在追求设计逼近最大似然性能的短LDPC码高效译码器过程中，我们采用了一种中继译码策略。神经最小和译码器启动译码过程，其产生的错误通过自适应有序统计译码进行后处理。本文着重阐述了支撑后处理的若干关键举措。首先，收集神经最小和译码器每次迭代的软信息，并将其输入卷积神经网络以增强比特可靠性估计。该过程能够识别易错比特，要么将其从最可靠基中排除，要么将其集中至最前端，这两者均有利于自适应有序统计译码。此外，由排序模式列表构成的译码路径将指导后处理过程。可调节的路径长度及对关联排序模式的精细化约束提供了多样化的复杂度管理手段。同时，引入新颖的辅助判据以显著减少自适应有序统计译码中候选码字列表的规模。大量实验结果与复杂度分析验证了配备这些创新技术的串行架构，可作为短LDPC码当前最优译码器的有力竞争者。