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A Method of Counting the Number of Cycles in LDPC Codes

For a given block length sequences 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 adding up all the number of cycles that contained in all possible combinations 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 their girth performance is not as good as the quasi-cyclic LDPC codes.