Ruling out small stopping sets and small girth in Tanner graph of QC-LDPC code

The existing constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate (BER) performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. ...