This paper proposes to use graph neural networks (GNNs) for equalization, that can also be used to perform joint equalization and decoding (JED). For equalization, the GNN is build upon the factor graph representations of the channel, while for JED, the factor graph is expanded by the Tanner graph of the parity-check matrix (PCM) of the channel code, sharing the variable nodes (VNs). A particularly advantageous property of the GNN is the robustness against cycles in the factor graphs which is the main problem for belief propagation (BP)-based equalization. As a result of having a fully deep learning-based receiver, joint optimization instead of individual optimization of the components is enabled, so-called end-to-end learning. Furthermore, we propose a parallel flooding schedule that further reduces the latency, which turns out to improve also the error correcting performance. The proposed approach is analyzed and compared to state-of-the-art baselines in terms of error correcting capability and latency. At a fixed low latency, the flooding GNN for JED demonstrates a gain of 2.25 dB in bit error rate (BER) compared to an iterative Bahl--Cock--Jelinek--Raviv (BCJR)-BP baseline.

翻译：本文提出使用图神经网络（GNN）进行均衡，并可同时实现联合均衡与译码（JED）。在均衡任务中，GNN基于信道的因子图表示构建；而在JED任务中，因子图通过信道编码的奇偶校验矩阵（PCM）的Tanner图进行扩展，共享变量节点（VNs）。GNN的一个显著优势在于其对因子图中环路的鲁棒性，而环路正是基于置信传播（BP）的均衡方法的主要问题。由于采用全深度学习接收机，本文实现了对组件的联合优化而非单独优化，即所谓的端到端学习。此外，我们提出一种并行洪泛调度方案，进一步降低了延迟，同时发现该方案还能提升纠错性能。本文对所提方法进行了分析，并在纠错能力和延迟方面与当前最先进的基线方法进行比较。在固定低延迟条件下，用于JED的洪泛GNN相比迭代式BCJR-BP基线在误码率（BER）上获得了2.25 dB的增益。