中文摘要：

Tanner图中的环分布影响着低密度校验码（LDPC,low-density parity-check code）译码算法的误码率性能,为快速计算出Tanner图中短环的数目,提出一种逐边递推基于矩阵运算的算法。首先定义5种基本图结构,算法在实施过程中可实现结构间的递推。与之前的研究工作相比,该算法对于同一环长提供多种方法进行计算,得到相同的计算结果,进一步证实算法的正确性。新算法不仅能计算出总的环数,还能给出每一条边参与的环数。该算法将时间复杂度从正比于码长N的3次方降为正比于码长的平方与变量节点平均度数D的乘积（D〈〈N）。对于大多数的LDPC码，计算环长为g、g＋2、g＋4的环数需要的时间仅为数秒。

英文摘要：

Loop distribution of Tanner graph affects the BER performance of low-density parity-check codes（LDPC） decoding. To count short cycles in the Tanner graph efficiently, a side by side recursion algorithm based on matrix computation was proposed. Firstly, 5 basic graph structures were defined to realize recursive calculate in the implementation process. Compared with previous works, the algorithm provided many methods for counting the same length of cycles. The same result confirmed the correctness of the algorithm. The new algorithm could not only calculate the total number of cycles, but also gave the number each edge participating in fixed-length cycles. Its complexity was proportional to the product of D and square of N, where D was the average degree of variable nodes, and N denoted the code length. For LDPC codes, D was far less than N. For most of the LDPC codes, the calculation for numbers of cycle-length g、g＋2、g＋4 was only several seconds.