In decoding linear block codes, it was shown that noticeable reliability gains can be achieved by introducing learnable parameters to the Belief Propagation (BP) decoder. Despite the success of these methods, there are two key open problems. The first is the lack of interpretation of the learned weights, and the other is the lack of analysis for non-AWGN channels. In this work, we aim to bridge this gap by providing insights into the weights learned and their connection to the structure of the underlying code. We show that the weights are heavily influenced by the distribution of short cycles in the code. We next look at the performance of these decoders in non-AWGN channels, both synthetic and over-the-air channels, and study the complexity vs. performance trade-offs, demonstrating that increasing the number of parameters helps significantly in complex channels. Finally, we show that the decoders with learned weights achieve higher reliability than those with weights optimized analytically under the Gaussian approximation.

翻译：在线性分组码译码中，研究表明通过向置信传播（Belief Propagation, BP）译码器引入可学习参数，可以获得显著的可靠性增益。尽管这些方法取得了成功，但仍存在两个关键未解问题：其一是缺乏对学习权重的解释，其二是缺乏对非加性高斯白噪声（AWGN）信道的分析。本文旨在通过剖析学习权重及其与底层码字结构的关系来弥合这一鸿沟。我们证明，权重受到码字中短环分布的显著影响。随后，我们考察这些译码器在非AWGN信道（包括合成信道和无线信道）中的性能，并研究复杂度与性能的权衡，表明增加参数数量在复杂信道中具有显著助益。最后，我们证明，在高斯近似下，采用学习权重的译码器比通过解析优化权重的译码器实现了更高的可靠性。