Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction ability and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, poses challenges in achieving extremely low error rates and the application of LDPC codes in scenarios demanding ultra high reliability. In this work, we propose training methods to optimize neural min-sum (NMS) decoders that are robust to the error-floor. Firstly, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two networks and train the post network to be specialized for uncorrected codewords that failed in the first network. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be implemented into current LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor.

翻译：低密度奇偶校验（LDPC）码因其强大的纠错能力和简单的译码过程已在通信系统中成功商业化。然而，LDPC码的错误平层现象（即误码率在某一水平停止快速下降）对实现极低误码率以及LDPC码在超高可靠性需求场景中的应用构成了挑战。本文提出针对神经最小和（NMS）译码器的优化训练方法，使其对错误平层具有鲁棒性。首先，利用集成网络的提升学习技术，将译码网络分为两个网络，使后网络专门针对前网络未能校正的码字进行训练。其次，为解决训练中的梯度消失问题，我们引入分块训练策略：在重训练前一块权重的同时，对当前块权重进行局部训练。最后，我们证明为不满足校验节点赋予不同权重，能以最少权重数有效降低错误平层。将这些训练方法应用于标准LDPC码，我们获得了相比其他译码方法最优的错误平层性能。所提出的NMS译码器仅通过新颖训练方法优化，无需额外模块即可嵌入现有LDPC译码器，且不产生额外硬件成本。源代码已开源至https://github.com/ghy1228/LDPC_Error_Floor。