突发错误是一种广泛存在于磁存储系统、深度衰落信道、电力线系统以及浅海水声等通信系统中的错误类型。空间耦合低密度奇偶校验码（Spatially Coupled Low Density Parity Check，SC-LDPC）码因其优异的“阈值饱和”特性而引起广泛关注，但在面临突发错误时会出现译码中断而导致译码性能恶化的情况。空间耦合广义LDPC（Spatially Coupled Generalized LDPC，SC-GLDPC）码通过在空间耦合结构中引入具有纠错能力的线性分组码替代单奇偶码，而呈现出空间耦合结构的阈值提升优势和广义约束带来的性能提升优势，但SC-GLDPC码在突发错误下的研究尚未展开。本文针对SC-GLDPC码，研究面向突发错误的SC-GLDPC码设计与性能分析，为存在突发错误的通信系统编码方案设计提供新思路。主要研究内容如下：

（1）针对一般突发删除信道，通过引入具有纠错能力的Hamming码替代无纠错能力的单奇偶校验码，提出了一种可对抗突发错误的基于Hamming码的SC-GLDPC码。为了评估SC-GLDPC码在一般突发删除信道下的渐进性能，推导了密度进化算法用于计算所提出的SC-GLDPC码的单个可纠最大突发删除长度。并利用该密度进化算法，以最大化可纠突发删除长度为目标，优化分量码列替换顺序，构造最优的抗突发删除错误的SC-GLDPC码。阈值结果表明，SC-GLDPC码的最大可纠突发删除长度远大于SC-LDPC码。所构造的有限长SC-GLDPC码在突发删除信道下的译码性能与阈值分析结果一致，优于传统的SC-LDPC码。

（2）脉冲噪声是一种广泛存在于电力线通信，水声通信及车载通信系统中的典型突发错误，会极大降低通信系统的可靠性。针对Class-A脉冲噪声信道，通过空间耦合结构中分别引入Hamming码和BCH码作为分量码，提出能够应对脉冲噪声的SC-GLDPC码。为了分析脉冲噪声信道下所构造的SC-GLDPC码的渐进性能，提出了一种基于外信息转移函数的阈值分析方法，推导了脉冲噪声信道下SC-GLDPC码变量节点和超级校验节点消息更新公式，计算了SC-GLDPC码的译码阈值。阈值结果表明，SC-GLDPC码的译码阈值较GLDPC码和SC-LDPC码具有显著提升。最后仿真了SC-GLDPC码在脉冲噪声信道下的译码性能，仿真结果表明所构造的SC-GLDPC码能有效对抗脉冲噪声。

Burst errors occur in a variety of communication systems, including magnetic storage systems, deep fading channels, power line systems, and underwater acoustic communication systems. Spatially coupled Low Density Parity Check (SC-LDPC) codes have attracted much attention due to their excellent "threshold saturation". However, when facing burst errors, the decoding chain of SC-LDPC codes will break up and the decoding performances will be dramatically degraded. By introducing error-correcting linear block codes into the spatial coupling structure instead of single parity check codes, spatially coupled generalized LDPC (SC-GLDPC) codes demonstrate the threshold improvements of the spatial coupling structure and the performance improvements due to the generalized constraints. However, no research on the performance of SC-GLDPC codes over burst error has been conducted. This paper studies the code design and performance analysis of SC-GLDPC code for burst errors, which provides a new viewpoint for the coding scheme design of communication systems with burst errors.

（1）For the general burst erasure channel, spatially coupled generalized LDPC code based on Hamming code with error correction instead of a single parity check code without error correction is proposed. To evaluate the asymptotic performance of SC-GLDPC code over the burst erasure channel, the density evolution algorithm is derived to calculate the maximum length of a single correctable burst. Moreover, the optimal sequence replacement order of the component code is obtained by maximizing the correctable burst erasure length using the proposed density evolution algorithm. Threshold analysis results show that the maximum correctable burst erasure length of SC-GLDPC codes is much larger than that of SC-LDPC codes. The finite length decoding performances of SC-GLDPC codes over the burst erasure channel are consistent with the threshold analysis results, which are superior to SC-LDPC codes.

（2）Impulsive noise, a typical type of burst error, is widely exhibited in power line communication, underwater acoustics communication, and vehicular communication systems, which can dramatically affect communication reliability. For Class-A impulse noise channels, SC-GLDPC codes are proposed to combat impulse noise by introducing error-correcting Hamming codes and BCH codes as component codes in the spatial coupling structure. To evaluate the asymptotic performance of the proposed SC-GLDPC codes over impulsive noise channels, a threshold analysis method based on the extrinsic information transfer functions was proposed. The message updates for variable nodes and super check nodes of SC-GLDPC codes over impulsive noise channels are derived, and the decoding thresholds of SC-GLDPC codes are calculated. The threshold results show that the decoding threshold of SC-GLDPC code is significantly improved compared to GLDPC codes and SC-LDPC codes. Finally, the decoding performance of SC-GLDPC code over impulsive noise channels is also simulated and the simulation results are consistent with the threshold results, which indicates that the proposed SC-GLDPC codes can effectively combat impulsive noise.

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