Research On LDPC Encoding/Decoding And Its Good Code's Structure Without Small Rings

A Low-Density Parity-Check (LDPC) Code is one kind of linear block code which is based on sparse parity-check matrix. This kind of code was originally proposed by Dr. Gallager in 1962, which can not attract a large amount of interests at that time. However, after decades of years, it is now rediscovered by Mackay and Neal, along with the enhancement of computer ability and the development of some relative theory such as gragh theory, BP algorithm, turbo codes and so on. It is also shown that the performance of LDPC codes is the closest codes to the Shannon limits in the world when combined with BP decoding algorithm.LDPC codes and Turbo codes are similar in many aspects, both can extremely approach to the Shannon limits in their own ways. The LDPC codes are relatively easy defined and can outperform the Turbo codes with sufficiently long block lengths. Its decoding complexity is also lower than turbo codes. Recently, LDPC codes have drawn the worldwide attentions in channel coding communit due to its high performance and strong potential applications in practice.This thesis offers a comprehensive study on the performance of LDPC codes and emphasizes on the complexity of encoding and the search and construction of good LDPC codes. The author does the analayis on many ways of LDPC codes's density evolution theory based on the random method and its enhancement of irregular LDPC codes and the quasi-cyclic LDPC codes based on the algebra's method. Through the study and research of the LDPC codes, the author presents a modified method of construction of LDPC codes using its essence of linear block code to realize the linear encoding. And in this method, in order to reduce the interference of relative informations when decoding, we avoid the appearance of 4-rings at the beginng of construction. So we make the modified method has the adventages in both linear complexity in encoding and good performances.