Coset-based QC-LDPC codes without small cycles

A simple and efficient search method based on the coset concept is proposed to construct (3, L) quasi-cyclic low-density parity-check (QC-LDPC) codes without small cycles. Compared with the random search method, the chance to find large-girth codes is remarkably increased for the new method. Compared with Tanner´s construction, the proposed method is much more flexible in the selection of row weight L. Some new codes are constructed with the shortest lengths compared with those constructed by the existing well-known methods. Simulation results show that the novel codes with moderate length perform well in the additive white Gaussian noise channel.