Evaluations of Good LDPC Codes Based on Generator Matrices

Since the weight and distance computations of LDPC codes is a NP problem, most presented evaluations of LDPC codes are based on the girth numbers of the codes, and 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 of the code length. Based on generation matrices, this paper develops an algorithm to estimate the upper bound of minimum weights and minimum distance of LDPC codes. The paper establishes the upper bounds of minimum weights and distances of LDPC codes by using the vectors of generation matrices, which is different from the presented probabilitistic search methods for the weights' and distances of LCPC 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.