Research On Principle And Decoding Algorithm Of Low-Density Parity-Check Codes

Designing codes with approaching Shannon's capacity performance and low coding and decoding complexity is a challenging and meaningful issue in channel coding field. Low-density parity-check code (LDPC codes) is a kind of asymptotic good codes that can approach Shannon's capacity with low complexity iterative decoding. In this thesis, the author proposed an algorithm to realize the two-way schedule and a new LDPC decoding algorithm called serial concatenated decoding algorithm based on thoroughly studying the principles of decoding for LDPC codes. Some simulation results and valuable conclusions have been interpreted in the thesis too.The following aspects are investigated in this thesis.1. The background and research situation of LDPC codes are presented and the current research results are introduced in the first part of the thesis. Graph presentation and sum-product algorithm are interpreted in detail. Linear coding theory and efficient constructing methods on LDPC codes are systemically interpreted later. A tool of analyzing the performance of LDPC decoder and designing the degree distribution of LDPC codes is introduced too.2. After a brief introduction to belief propagation algorithm and a close research on the message flowing schedule, a new serial concatenated decoding method of LDPC codes based on the matrix decomposition and the two-way schedule is proposed in this thesis. It aims at gaining fast convergence with the same complexity as the conventional belief propagation algorithm. Density evolution theory analysis and programming simulation results show that this new algorithm has fast convergence speed and good performance.3. In the actual communication environment, channel bandwidth is often limited. Bandwidth efficient multilevel coded modulation system based on LDPC codes is described in the last part of this thesis. Furthermore, the designing method of combining component code rate and degree distribution is introduced.