Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. 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 integrated into existing 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实现商业化。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——对其实现极低误码率以及在高可靠性场景中的应用提出了挑战。本文针对神经最小和（NMS）译码器提出训练方法以消除错误平层效应。首先，通过利用集成网络的提升学习技术，我们将译码网络划分为两个神经译码器，并对后一个译码器进行专门训练，使其处理前一个译码器未能纠正的错误字。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：在对前一块权重进行再训练的同时，局部训练后一块权重。最后，我们证明对不满足校验节点赋予不同权重能有效降低错误平层，且所需权重数量极少。通过将这些训练方法应用于标准LDPC码，我们实现了优于其他译码方法的错误平层性能。所提出的NMS译码器仅通过新颖的训练方法优化，无需额外模块，即可集成到现有LDPC译码器中且不增加硬件成本。源代码见 https://github.com/ghy1228/LDPC_Error_Floor 。