Abstract: By the method for investigating the relation between parity-check matrixes and cycles of associated Tanner graphs proposed by Chen et al., the one-to-one correspondence between k-row-combinations satisfying a certain condition in a parity-check matrix of grith k and shortest cycles in the associated Tanner graph is proved. As a consequence, the algorithm for counting the shortest cycels of Tanner graphs proposed by Chen et al. is improved. The improved algorithm is as accurate as the original one while omitting one of the main steps.

Key words: low-density parity-check (LDPC) code, Tanner graph, shortest cycle, 2k-cycle-matrix