LDPC Codes Based on Berlekamp-Justesen Codes with Large Stopping Distances

By employing a class of q-ary cyclic codes, i.e., Berlekamp-Justesen (B-J) codes, as base codes, we obtain two classes of structured LDPC codes by q-tuple and (q - 1)-tuple substitutions. These constructions can be viewed as generalizations of Reed-Solomon based LDPC codes proposed by Djurdjevic et. al. The B-J based LDPC codes, which could be regular or irregular according to the adjustment of three parameters, have much flexibility in choices of the code length, rate and minimum/stopping distance. Furthermore, the minimum distances and stopping distances of the B-J based LDPC codes are analyzed. We show that the stopping distance of a B-J based LDPC code is not smaller than the best known lower bound of its minimum distance. The B-J based LDPC codes perform well under iterative decoding and manifest low error-floors in simulations which could be explained in one respect by their large minimum distances and stopping distances