A new algorithm of counting the number of small stopping sets and girth in QC-LDPC Codes

It is well known that the performance of low-density parity check (LDPC) codes under iterative decoding is determined by certain combinatorial structures (such as stopping sets and girth) in the Tanner graph. The difficulty in enumerating all possible combinations of the columns may prevent an efficient search of good LDPC codes with small stopping sets and girth. To solve the problem, this paper presents a new algorithm of counting the number of small stopping sets and girth by analyzing the shapes of the cycles of Tanner graph in parity check matrix for designing good LDPC codes which is less complex than the existing algorithms. This method can be used effectively to evaluate the performance of LDPC codes according to their small stopping sets and girth distributions.