Searching the minimum distances of LDPC codes

To find the minimum distance computation of LDPC codes is a NP problem, there has been no simple way to obtain the minimum distance of LDPC codes because of the code length being very long. To provide a solution to deal with this hard problem, this paper develops an algorithm to estimate the weights and distance of LDPC codes based on generator matrices. The paper establishes the upper bounds of weights and distances of LDPC codes by using the vectors of generator matrices, which is different from the existed 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 can obtain some LDPC codes of great distances and being free girth 4. Simulations verify the algorithms to be valid.