Construction Methods of High Performance LDPC Codes

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Though the LDPC (Low Density Parity Check) codes are known as the codes to attain very good and close performance to the Shannon's limit, there still remain some basic problems to be resolved: e.g., (1) to derive detailed described code ensembles and evaluate their performance efficiently, (2) to construct LDPC codes with algebraic structure which are important in practical implementation.To solve these two basic problems, we in this research have proposed (1) a new class of Multi-Edge type LDPC code ensembles and an efficient DE (Density Evolution) for the proposed ensembles, (2) new modified expander codes and MDS (Maximum Distance Separable) array codes which are easy to implement as well as high performance.In the fiscal year 2006, (1) we developed DE (Density Evolution) for the new class of Multi-Edge type LDPC code ensembles which are constructed based on the newly found symmetry property, (2) proposed Justesen like modified expander codes which are decodable in linear time with the minimum distance repeat decoding and having asymptotically good performance.In the fiscal year 2007, (1) for the proposed new class of Multi-Edge type LDPC code ensembles, we have derived the weight distributions and the Stopping Set distributions and confirmed the effectiveness of the proposed code ensembles, (2) by comparing the proposed codes with the corresponding conventional ones we have found that the proposed codes exhibit sufficiently good performance and are thought to be very effective in practice.