一种低密度奇偶校验码的环数统计方法

A Method of Counting the Number of Cycles in LDPC Codes

对于Tanner图中给定码长的序列,LDPC码的短环对码的性能有重要影响。本文在分析LDPC码在Tanner图中的环在校验矩阵中的形状的基础上,提出了一种统计LDPC码中不同环长的环数的方法。首先对校验矩阵中一定数目的行组合中的环数进行统计,然后将所有行组合中的环数相加即得到校验矩阵中的环数。该方法可根据LDPC码的短环分布情况对其性能进行评估。应用提出的方法分别对MacKay的随机码和Fossorier的准循环码进行了环数统计。BER性能显示,尽管随机码环数特性比准循环码要差,但它的误码率性能比准循环码要好。

For a given block length sequence of the underlying Tanner graph （TG） ,the short circles of low-density parity check （LDPC） codes can have considerable variation in performance. By analyzing the shapes of the cycles of TG in parity check matrix, this paper presents a method of counting the number of 4-cycles ,6-cycles, 8-cycles and 10-cycles. Taking out a certain number of rows for different cycles, counting the number of cycles contained in these rows, then add up all the number of cycles that contained in all possible combination of the rows in the matrix, and we can get the number of cycles in the matrix. This method can be used effectively to evaluate the performance of LDPC codes according to their short circles distributions. Applying this method, we counting the number of cycles in the random LDPC codes and the quasi-cyclic LDPC codes, the BER performance shows that the random LDPC codes outperform the quasi-cyclic LDPC codes although it＇ s girth performance is not as good as the quasi-cyclic LDPC codes.