基于模拟退火算法构造girth-12（3，5）和（3，6）-规则QC—LDPC码

文章提出了一种基于模拟退火算法的准循环校验矩阵设计方法。首先，建立了一类具有特殊结构的准循环校验矩阵的设计步骤与模拟退火算法中迭代初始解、目标函数和邻域结构之间的联系，然后利用有记忆的模拟退火算法设计出了两个准循环校验矩阵。利用这两个矩阵，文章对于任意P≥217构造出了girth-12（3，5）规则QC—LDPC码；对于任意P≥449构造出了girth．12（3，6）规则QC-LDPC码。与已知的最好结果相比，该文将girth-12（3，5）和（3，6）规则QC—LDPC码连续存在的码长下限分别降低了420比特和492比特。

Construction of Girth-12 （3,5） - and （3,6） -Regular QC-LDPC Codes Based on Simulated Annealing Algorithm

A design method is presented by the simulated annealing （SA） algorithm to construct parity-check matrices of quasi-cyclic （QC） low-density parity-check （LDPC） codes. A novel bridge is created between the designing steps of a type of QC-parity-check matrices subjected to some special structural constrains and the individual elements of SA algorithm, such as iterative initial solution, objective function and neighboring structure. Base on this new idea, two interesting QC-parity-check matrices are successfully constructed from the SA algorithm with an additional memory. By the double matrices, a family of girth-12 （3,5）-regular QC-LDPC codes and a family of girth-12 （3,6）-regular QC-LDPC codes are found with arbitrary P≥217 and arbitrary P≥449 ,respectively. Compared with the existing best results, the lower bounds for the consecutive length of girth-12 （3,5） -and （3,6） -regular QC-LDPC codes are decreased by 420 bits and 492 bits, respectively, according the two new matrices.