空间耦合LDPC（Spatially Coupled LDPC, SC-LDPC）码所具有的“阈值饱和”特性和低复杂度结构特性，使其成为未来无线通信系统信道编码方案的有力竞争者。然而当面临突发删除错误时，常规的单链SC-LDPC码会出现译码中断，导致译码性能急剧下降，而这个问题无法通过增加耦合链的长度来解决，这就迫切需要设计一种能够有效对抗突发删除错误的SC-LDPC码。为此，本文针对突发删除信道提出了基于多条耦合链连接构造多维SC-LDPC码的方法，以此来提升其对抗突发删除错误的能力，为突发删除信道下SC-LDPC码的设计提供新思路。主要研究内容如下：

基于SC-LDPC码优异的“阈值饱和”特性，结合非对称边展开方式，提出了一种可逼近突发删除信道容量限的并联SC-LDPC码的构造方法。该码是通过边交换将两条非对称SC-LDPC耦合链进行并行连接构造得到。一方面由于非对称边展开方式使得SC-LDPC码具有更大的停止集最小基数，有益于其提升突发删除纠错能力。另一方面边交换的连接方式在不改变度分布和不增加复杂度的情况下，可为两条耦合链在面对突发删除错误时提供信息支持，避免其中一条耦合链出现译码中断，从而提升了对抗突发删除错误的能力。接着，针对并联SC-LDPC码，推导了用于阈值分析的密度进化算法。分析结果表明，并联SC-LDPC码的最大可纠突发删除长度可逼近于容量限，且远大于非对称SC-LDPC码和常规的单链SC-LDPC码。在突发删除信道下的有限长性能仿真结果与阈值分析结果相吻合，验证了并联SC-LDPC码对抗突发删除错误的有效性。

基于空间耦合码的原模图结构特性，提出了另一种可逼近突发删除信道容量限的串联SC-LDPC码的构造方法。该码是通过边交换将两条常规的SC-LDPC耦合链进行串行连接构造得到。不同于并联SC-LDPC码的是，一方面交换边的边数不同。对于每个耦合位置，并联SC-LDPC码交换边数取决于两条耦合链的最小变量节点个数，而串联SC-LDPC码取决于变量节点的度。另一方面交换边的连接位置不同。对任意耦合位置，并联SC-LDPC码交换边仅连接到另一条链的同一位置，而串联SC-LDPC码交换边连接到另一条链耦合宽度内满足约束条件的位置上。并推导了用于计算串联SC-LDPC码在突发删除信道下单个最大可纠突发删除长度的密度进化算法。阈值分析结果表明，串联SC-LDPC码的阈值与容量限间隔非常小，且远优于非对称SC-LDPC码和常规的单链SC-LDPC码。有限长性能仿真结果表明，所设计的串联SC-LDPC码在突发删除信道下的性能较非对称SC-LDPC码和常规的单链SC-LDPC码有显著提升。

Spatially coupled low density parity check (SC-LDPC) codes are promising candidates for channel coding schemes in future wireless communication systems due to their "threshold saturation" properties and low complexity structures. However, when facing burst erasures, the decoding performances of the conventional single-chain SC-LDPC codes will be dramatically degraded due to the interruption of decoding chain, and this problem cannot be solved by increasing the length of the coupling chain. In this paper, we propose the multi-dimensional SC-LDPC codes constructed by connecting multiple coupling chains to improve their capabilities to combat burst erasures, which provides a new viewpoint for the design of SC-LDPC codes over burst erasure channels. The main works are as follows:

Based on the "threshold saturation" properties of SC-LDPC codes, a capacity-approaching parallelly connecting SC-LDPC (PC-SC-LDPC) code is proposed by utilizing the asymmetric edge expansion for the burst erasure channel. The PC-SC-LDPC code is constructed by connecting two asymmetric SC-LDPC coupling chains in parallel through edge exchanges. On one hand, the asymmetric edge expansion makes the SC-LDPC code possess larger minimal cardinality of stopping sets, which is beneficial to improve the burst erasures correction capability. On the other hand, the edge exchanges can provide information support for both coupling chains in the face of burst erasures without changing the degree distribution and increasing the complexity, which will avoid the decoding termination of one coupling chain and thus improve the ability to combat burst erasures. Moreover, density evolution algorithm is derived to obtain the thresholds of the proposed PC-SC-LDPC codes. The analysis results show that the maximum correctable burst erasure lengths of PC-SC-LDPC codes can approach the capacity limits and are also much larger than those of the asymmetric SC-LDPC codes and the conventional single-chain SC-LDPC codes. Finite length performances over the burst erasure channels can fit well to the threshold analysis results, which verifies the effectiveness of the proposed PC-SC-LDPC codes against burst erasures.

Based on the protographs of the SC-LDPC codes, an alternative capacity-approaching serial connecting SC-LDPC (SC-SC-LDPC) code is proposed, which is constructed by serially connecting two conventional SC-LDPC coupling chains through edge exchanges. Different from the PC-SC-LDPC codes, one is that the number of edges used for edge exchanges is different. For each coupling position, the number of the exchanged edges of PC-SC-LDPC codes depends on the minimum number of variable nodes in two chains, while for the SC-SC-LDPC code it depends on the degrees of variable nodes. The other is that the positions where the edge exchanges occurred are different. For any coupling position, the exchanged edges of PC-SC-LDPC codes are connected to the same position of another chain, while the exchanged edges of SC-SC-LDPC codes are connected to the positions that satisfies the constraints within the coupling width of another chain. Density evolution algorithm for calculating the single maximum correctable burst length of SC-SC-LDPC code under burst erasure channel is derived. Threshold analysis results show that the gaps between the thresholds and capacity limits are very small and the thresholds are much better than those of the conventional SC-LDPC codes and the asymmetric SC-LDPC codes. Finite-length performance simulation results show that the performances of the proposed SC-SC-LDPC codes over burst erasure channels can be significantly improved compared to SC-LDPC codes and asymmetric SC-LDPC codes.

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