Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this article, we consider nested array-based spatially coupled low-density parity-check (SC-LDPC) codes and propose a line-counting based optimization scheme for minimizing the number of dominant absorbing sets in order to improve its performance in the high signal-to-noise ratio regime. Since the parity-check matrices of different nested sub-codes partially overlap, the optimization of one nested sub-code imposes constraints on the optimization of the other sub-codes. To tackle these constraints, a multi-step optimization process is applied first to one of the nested codes, then sequential optimization of the remaining nested codes is carried out based on the constraints imposed by the previously optimized sub-codes. Results show that the order of optimization has a significant impact on the number of dominant absorbing sets in the Tanner graph of the code, resulting in a trade-off between the performance of a nested code structure and its optimization sequence: the code which is optimized without constraints has fewer harmful structures than the code which is optimized with constraints. We also show that for certain code parameters, dominant absorbing sets in the Tanner graphs of all nested codes are completely removed using our proposed optimization strategy.

中文翻译：

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基于嵌套阵列的空间耦合 LDPC 码

线性嵌套代码，其中两个或多个子代码嵌套在全局代码中，已被提议作为可靠多终端通信的候选。在本文中，我们考虑了基于嵌套阵列的空间耦合低密度奇偶校验 (SC-LDPC) 码，并提出了一种基于行计数的优化方案，用于最小化主要吸收集的数量，以提高其在高信噪比制度。由于不同嵌套子码的奇偶校验矩阵部分重叠，一个嵌套子码的优化对其他子码的优化施加了约束。为了解决这些约束，首先对嵌套代码之一应用多步优化过程，然后根据先前优化的子代码施加的约束对剩余的嵌套代码进行顺序优化。结果表明，优化的顺序对代码的Tanner图中的主导吸收集的数量有显着影响，导致嵌套代码结构的性能与其优化序列之间的权衡：被优化的代码与使用约束优化的代码相比，无约束具有更少的有害结构。我们还表明，对于某些代码参数，使用我们提出的优化策略完全去除了所有嵌套代码的 Tanner 图中的主要吸收集。结果表明，优化的顺序对代码的Tanner图中的主导吸收集的数量有显着影响，导致嵌套代码结构的性能与其优化序列之间的权衡：被优化的代码与使用约束优化的代码相比，无约束具有更少的有害结构。我们还表明，对于某些代码参数，使用我们提出的优化策略完全去除了所有嵌套代码的 Tanner 图中的主要吸收集。结果表明，优化的顺序对代码的Tanner图中的主导吸收集的数量有显着影响，导致嵌套代码结构的性能与其优化序列之间的权衡：被优化的代码与使用约束优化的代码相比，无约束具有更少的有害结构。我们还表明，对于某些代码参数，使用我们提出的优化策略完全去除了所有嵌套代码的 Tanner 图中的主要吸收集。