Machine learning based approaches are being increasingly used for designing
decoders for next generation communication systems. One widely used framework
is neural belief propagation (NBP), which unfolds the belief propagation (BP)
iterations into a deep neural network and the parameters are trained in a
data-driven manner. NBP decoders have been shown to improve upon classical
decoding algorithms. In this paper, we investigate the generalization
capabilities of NBP decoders. Specifically, the generalization gap of a decoder
is the difference between empirical and expected bit-error-rate(s). We present
new theoretical results which bound this gap and show the dependence on the
decoder complexity, in terms of code parameters (blocklength, message length,
variable/check node degrees), decoding iterations, and the training dataset
size. Results are presented for both regular and irregular parity-check
matrices. To the best of our knowledge, this is the first set of theoretical
results on generalization performance of neural network based decoders. We
present experimental results to show the dependence of generalization gap on
the training dataset size, and decoding iterations for different codes.

本文研究神经信念传播解码器的泛化能力，利用机器学习方法设计下一代通信系统的译码器，提高传统解码算法的性能。通过理论与实验结果给出了解码器的泛化缺口，以及其与代码参数、解码迭代次数、训练数据集大小等的关系。

神经置信传播译码器的泛化界限

Generalization Bounds for Neural Belief Propagation Decoders

We study the application of the factor graph framework for symbol detection
on linear inter-symbol interference channels. Cyclic factor graphs have the
potential to yield low-complexity symbol detectors, but are suboptimal if the
ubiquitous sum-product algorithm is applied. In this paper, we present and
evaluate strategies to improve the performance of cyclic factor graph-based
symbol detection algorithms by means of neural enhancement. In particular, we
apply neural belief propagation as an effective way to counteract the effect of
cycles within the factor graph. We further propose the application and
optimization of a linear preprocessor of the channel output. By modifying the
observation model, the preprocessing can effectively change the underlying
factor graph, thereby significantly improving the detection performance as well
as reducing the complexity.

本文研究了因子图框架在线性符号干扰通道上的符号检测应用，并提出了利用神经增强的策略来改善循环因子图基于符号检测算法的性能的方法。特别是，在因子图中应用神经置信传播可有效消除循环的影响。此外，我们还提出了对信道输出的线性预处理应用和优化，可以有效地改变底层因子图，从而显著提高检测性能并降低复杂性。

基于因子图的符号检测神经增强

Neural Enhancement of Factor Graph-based Symbol Detection

We consider near maximum-likelihood (ML) decoding of short linear block codes
based on neural belief propagation (BP) decoding recently introduced by
Nachmani et al.. While this method significantly outperforms conventional BP
decoding, the underlying parity-check matrix may still limit the overall
performance. In this paper, we introduce a method to tailor an overcomplete
parity-check matrix to (neural) BP decoding using machine learning. We consider
the weights in the Tanner graph as an indication of the importance of the
connected check nodes (CNs) to decoding and use them to prune unimportant CNs.
As the pruning is not tied over iterations, the final decoder uses a different
parity-check matrix in each iteration. For Reed-Muller and short low-density
parity-check codes, we achieve performance within 0.27 dB and 1.5 dB of the ML
performance while reducing the complexity of the decoder.

本文提出了一种使用机器学习来定制超完备校验矩阵的方法，通过裁剪不重要的检测节点并优化 Tanner 图中的权重，每个迭代使用不同的校验矩阵，从而在短线性块码上，实现比 BP 译码更好的性能且减少了解码器的复杂度。