一种无短停止距离及短环的准循环LDPC码构造方法

短停止距离及短环的存在使准循环LDPC（QC-LDPC）码的BER性能比随机构造的LDPC码的性能差,然而现有的准循环LDPC（QC-LDPC）码设计方法并没有同时考虑消除短停止距离和短环.为此,本文给出构造准循环LDPC码无短停止距离（停止距离为2和3）和无短环（4环和6环）的充要条件,解决了构造任意长度无短停止距离且无短环的QC-LDPC码的设计问题,为系统分析法构造校验矩阵提供了理论依据.在有效消除了短停止距离和短环的同时,使QC-LDPC码具有较大的最小汉明距离.实验结果表明,在中短码和长码时按照本文所提出定理设计的QC-LDPC码具有明显优于随机构造的LDPC码性能,且无错误平层.

Construction of Quasi-Cyclic LDPC Codes Without Small Stopping Sets and Small Cycles

The existing design of quasi-cyclic low-density parity-check（short for QC-LDPC） codes has not considered the problems of small stopping sets and small cycles together,while their existences will lead to the BER performance of QC-LDPC codes to be much poorer than that of the randomly constructed LDPC codes even decoding failure.To solve the problem,some theorems of the QC-LDPC codes without small stopping sets and small cycles were proposed which provide a theoretical basis for the construction of parity-check matrix by analysis method;meanwhile,good QC-LDPC codes without small stopping sets and small cycles were designed.Since preventing the small stopping sets and small cycles also prevents a low minimum distance,our construction method also leads to QC-LDPC codes with a higher minimum distance.The simulation results show that the QC-LDPC codes can effectively avoid specified stopping sets and small cycles and achieve good coding and decoding property due to the proposed constructions.