Research On The Performance Of LDPC Code And Its Serial Concatenated Code

The linear block code is called a binary low-density parity-check code if it is based on a sparse parity-check matrix. This sort of code was originally proposed by Dr. Gallager in 1962, which had not attracted a large amount of interest 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 graph theory, BP algorithm, turbo codes and so on. It is also proved that the performance of LDPC codes is very close to the Shannon limits when combined with BP algorithm.LDPC codes and turbo codes are similar in many aspects, both can extremely approach to the Shannon limits by their unique ways. The performance of turbo codes is better than any other codes at low SNR. While LDPC codes are relatively easy to be characterized, and can outperform turbo codes with sufficiently long block lengths. Its decoding complexity is also lower than turbo codes. In recent years, LDPC codes have attracted the worldwide attentions in information theory and channel coding communities due to its impressive performance and great potentials in application.This thesis offers a comprehensive study on the performance of LDPC codes. The author first presents a new method for construction of irregular LDPC codes based on generator matrix in order to reduce encoding complexity, including systematic and non-systematic irregular LDPC codes. The performance simulations are carried out over AWGN and Rayleigh channels, and the obtained results are also compared with those acquired by the traditional approach under the same conditions. Then, we adopt the optimized irregular LDPC codes based on generator matrix to construct product codes. Meanwhile, performance simulations are also made and the comparisons between the designed product codes and LDPC codes are performed under the identical conditions. Finally, in order to further improve the performance and reduce the decoding complexity, we investigate the theory of the cyclic codes, in particular for BCH and RS codes. The proposed the serial concatenations of BCH and LDPC codes are extensively investigated for their performance over an AWGN channel. Performance comparisons are also made with the single code schemes. These concatenated schemes are of extremely important for some new wireless communications standards, such as European and Chinese standards for the high definition TV (HDTV).