Abstract
In this thesis, we proposed an effective method to construct practical LDPC codes with low error floors. We first consider a class of LDPC codes, called LUmk codes each of which is obtained by removing edges and nodes of the Tanner graph of an LU code and may have arbitrary large girth and high code rate. We derived a lower bound for the stopping distance of an LUmk code and developed a simple method to choose some edges and nodes which should be removed and get a small code ensemble with relatively low error floors from the original LUmk code ensemble.