In research on spatially-coupled low-density parity-check (SC-LDPC) codes, rate-loss of SC-LDPC codes is one of the main issues to be addressed. One way to mitigate the rate-loss is to attach additional variable nodes with an irregular degree distribution, where the degree distribution is optimized with a constraint that the belief propagation (BP) threshold should not be degraded by attaching variable nodes. However, it is observed that the degree distribution obtained with the BP threshold constraint induces degradation of the finite-length performance. In order to address the problem, we propose new optimization methods to attach additional variable nodes while minimizing performance degradation. The proposed optimization methods are based on several design techniques including the scaling law, local threshold, expected graph evolution, differential evolution algorithms, the use of a protograph structure, and puncturing codewords. Using the optimized structure for additional variable nodes, the rate-loss of SC-LDPC codes can be reduced by more than 53% without sacrificing the finite-length performance. It is also shown that the rate-loss mitigation can be translated into a performance improvement if the proposed and the conventional SC-LDPC codes are compared at the same code rate.

中文翻译：

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在不降低性能的情况下缓解 SC-LDPC 码的速率损失

在空间耦合低密度奇偶校验（SC-LDPC）码的研究中，SC-LDPC码的速率损失是需要解决的主要问题之一。减轻率损失的一种方法是附加具有不规则度分布的附加变量节点，其中度分布在约束条件下进行优化，即置信传播 (BP) 阈值不应因附加变量节点而降低。然而，观察到使用 BP 阈值约束获得的度分布会导致有限长度性能的下降。为了解决这个问题，我们提出了新的优化方法来附加额外的变量节点，同时最大限度地减少性能下降。所提出的优化方法基于多种设计技术，包括缩放定律、局部阈值、预期图演化、差分进化算法、原型结构的使用和打孔码字。使用额外可变节点的优化结构，在不牺牲有限长度性能的情况下，SC-LDPC码的速率损失可以降低53%以上。还表明，如果在相同的码率下比较所提出的和传统的 SC-LDPC 码，速率损失缓解可以转化为性能改进。