A construction of LDPC codes with low error floors

In this paper, we propose an effective method to construct practical LDPC codes with low error floors. We first consider a class of LDPC codes, called masked Lazebnik-Ustimenko (LU) codes each of which is obtained by removing edges and nodes from the Tanner graph of an LU code and may have arbitrary large girth and high code rate. We then derive a lower bound for the stopping distance of a masked LU code and develop a simple method to further purge edges and nodes to obtain a small code ensemble with relatively lower error floors than the original masked LU code ensemble.