基于PEG算法的准循环扩展LDPC码构造  

Quasi-cyclic extension based on PEG algorithm for construction of LDPC codes

作　　者：雷菁[1] 王建辉[1] 唐朝京[1] 

机构地区：[1]国防科学技术大学电子科学与工程学院,湖南长沙410073

出　　处：《通信学报》2008年第9期103-110,共8页Journal on Communications

基　　金：国家自然科学基金资助项目(60572176)~~

摘　　要：推导证明了准循环结构的LDPC码(low-density parity-check code)一致校验矩阵与其对应Tanner图环结构之间的一些重要关系。在此基础上提出了一种基于PEG(progress edge growth)算法的准循环扩展LDPC码构造算法,利用PEG算法产生基矩阵,再对基矩阵进行准循环扩展。该扩展算法可以在不改变基矩阵度分布比例情况下,有效消除基矩阵中的短环。仿真结果表明,在码长相同、码率和度分布近似情况下,新算法得到的码在经典BP和MS译码算法下性能不亚于PEG等方法构造的码。通过对比分析认为,在给定度分布的情况下,优化设计的环结构可明显改善译码性能,此算法利用准循环码环结构交叠较少特点,较好地实现了编码复杂度和译码性能之间的统一。Several important relations between the cycle structure on the Tanner graph and the parity-check matrix H of LDPC codes were proved. A new algorithm for constructing LDPC codes was proposed that introduced quasi-cyclic extension method to PEG algorithm. After a basic matrix was constructed with PEG algorithm, circulant permutation matrices would replace the ＂1＂s in the basic matrix. The new method could eliminate effectively the short cycles in the basic matrix without changing the degree distribution fraction of the basic matrix. Simulations show that the quasi-cyclic extended codes based on PEG algorithm have as good error correcting performance as the LDPC codes generated by PEG algorithm in the same conditions of code length ,rate, degree distribution and decoding algorithm. The conclusion of contrastive analysis is that well-chosen cycle structures can improve the decoding performance obviously under the given degree distribution. The proposed algorithm can offer a good performance and low encoding complexity synchronously by taking advantage of the quasi-cyclic code＇s characteristic that its parity-check matrix H has less superposition within the cycles.

关 键 词：PEG算法 准循环扩展 循环置换矩阵 编码复杂度 本地围长 环结构 

分 类 号：TN911[电子电信—通信与信息系统]