Lower bounds of weights and distances of good LDPC codes

Abstract

Since the distance computation is a NP problem, most presented evaluations of LDPC codes are mainly based on the girth numbers of the codes. The computation for the distance of the codes is also depended on the girth numbers. There has been no simple way to obtain the distance of LDPC codes because the code length is very long. Based on generation matrices, this paper develops an algorithm to estimate the weights and distance of LDPC codes. The paper establishes the lower bounds of weights and distances of LDPC codes by using the vectors of generation matrices, which is different from the presented probabilistic search methods for the weights' and distances of LDPC codes. The proposed algorithm can greatly reduce the searching time of weights and distances. Applying the algorithm we find that some LDPC codes get good BER performance although they are only free girth 4 but of great distances. Simulations verify the algorithms to be valid. (5 pages)