This paper presents a new type of globally-coupled low-density parity-check (GC-LDPC) codes whose base matrix has a cyclic structure in the global part. Therefore, the resulting codes are referred to as tail-biting GC-LDPC (TB-GC-LDPC) codes. We propose two methods to construct TB GC quasi-cyclic LDPC (TB-GC-QC-LDPC) codes. For the first method, we extract a replicated version of a constructed base matrix and mask it with a designed masking matrix. Compared to the conventional construction methods, this method provides more flexibility in code length for TB-GC-QC-LDPC codes. The second method is based on designing the incidence matrix of a special type of packings. Examples show that the constructed TB-GC-QC-LDPC codes perform well over the additive white Gaussian noise channel (AWGNC) and the binary erasure channel (BEC). The asymptotic performance of TB-GC-LDPC ensembles over BECs are also analyzed by resorting to density evolution. Moreover, numerical results show that TB-GC-LDPC ensembles can achieve better flooding-schedule decoding (FSD) thresholds than the corresponding GC-LDPC ensembles with a similar structure. With sufficient decoding iterations in the global phase, the local/global two-phase iterative decoding (TPD) thresholds of the TB-GC-LDPC ensembles significantly outperform those of the corresponding GC-LDPC ensembles as well.

中文翻译：

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咬尾全局耦合的 LDPC 码

本文提出了一种新型的全局耦合低密度奇偶校验（GC-LDPC）码，其基矩阵在全局部分具有循环结构。因此，产生的代码被称为咬尾GC-LDPC（TB-GC-LDPC）代码。我们提出了两种构造TB GC准循环LDPC（TB-GC-QC-LDPC）码的方法。对于第一种方法，我们提取构建的基础矩阵的复制版本，并用设计的掩码矩阵对其进行掩码。与传统的构造方法相比，该方法为TB-GC-QC-LDPC码提供了更大的码长灵活性。第二种方法基于设计特殊类型填料的关联矩阵。示例表明，构建的 TB-GC-QC-LDPC 码在加性高斯白噪声通道 (AWGNC) 和二进制擦除通道 (BEC) 上表现良好。TB-GC-LDPC 集成在 BEC 上的渐近性能也通过密度演化进行了分析。此外，数值结果表明，与具有类似结构的相应 GC-LDPC 集成相比，TB-GC-LDPC 集成可以实现更好的泛洪调度解码（FSD）阈值。通过在全局阶段进行足够的解码迭代，TB-GC-LDPC 集成的局部/全局两阶段迭代解码 (TPD) 阈值也显着优于相应的 GC-LDPC 集成。