A cyclic-shift based method for counting cycles of quasi-cyclic LDPC codes

M. Fossorier proposed how to determine the necessary and sufficient conditions for the existence of cycles in the Tanner graph of quasi-cyclic LDPC (QC-LDPC) codes, which has been widely investigated in the study of LDPC codes. This paper presents some new necessary and sufficient conditions for the existence of cycles with arbitrary lengths and proposes a simple and novel method for counting cycles of QC-LDPC codes based on the improved conditions. Numerical results show that, compared with the existing methods, the presented method is effective and feasible and can enumerate cycles of QC-LDPC codes in a cyclic-shift way. This paper presents some new necessary and sufficient conditions for the existence of cycles with arbitrary lengths and proposes a simple and novel method for counting cycles of QC-LDPC codes based on the improved condition. Compared with the existing methods, the presented method is effective and feasible and can enumerate cycles of QC-LDPC codes in a cyclic-shift way.image