A new construction of irregular LDPC convolutional codes with cycle removal

In this paper, a new construction of irregular low-density parity-check convolutional codes (LDPC-CCs) is presented. Both upper and lower bounds on the free distance are derived as well. Compared with previously constructed irregular LDPC-CCs, our design can not only avoid a girth less than 8 but also provide an enlarged free distance. Since some undesired cycles occur due to the binomial terms in the parity-check matrices of general LDPC-CCs, we provide a specific procedure to remove this kind of length-8 cycles. It can also be applied to our irregular construction. Simulation results show that the codes based on the new construction and the cycle-removal procedure can achieve better bit-error-rate performance and a lower error-floor.