Deep neural network (DNN)-based channel decoding is widely considered in the literature. The existing solutions are investigated for the case of hard output, i.e. when the decoder returns the estimated information word. At the same time, soft-output decoding is of critical importance for iterative receivers and decoders. In this paper, we focus on the soft-output DNN-based decoding problem. We start with the syndrome-based approach proposed by Bennatan et al. (2018) and modify it to provide soft output in the AWGN channel. The new decoder can be considered as an approximation of the MAP decoder with smaller computation complexity. We discuss various regularization functions for joint DNN-MAP training and compare the resulting distributions for [64, 45] BCH code. Finally, to demonstrate the soft-output quality we consider the turbo-product code with [64, 45] BCH codes as row and column codes. We show that the resulting DNN-based scheme is very close to the MAP-based performance and significantly outperforms the solution based on the Chase decoder. We come to the conclusion that the new method is prospective for the challenging problem of DNN-based decoding of long codes consisting of short component codes.

翻译：深度神经网络（DNN）信道译码在文献中被广泛研究。现有方案主要针对硬输出情形，即译码器返回估计信息字。然而，软输出译码对于迭代接收机与译码器至关重要。本文聚焦于基于软输出的DNN译码问题。我们以Bennatan等人（2018年）提出的基于伴随式的方法为基础，对其进行改进以在加性高斯白噪声（AWGN）信道中提供软输出。新译码器可视为计算复杂度更低的MAP译码器近似。我们讨论了面向联合DNN-MAP训练的正则化函数，并比较了[64, 45] BCH码的分布结果。最后，为展示软输出质量，我们采用以[64, 45] BCH码作为行码和列码的turbo乘积码进行验证。结果表明所提DNN方案性能与基于MAP的方案非常接近，并且显著优于基于Chase译码器的方案。我们得出结论：对于由短分量码构成的长码DNN译码这一挑战性问题，新方法具有应用前景。