Theoretical Analysis Of Low Density Parity Check Codes And Applied Research In Image Transmission

In 1962,Gallager proposed a special linear grouping codes with a very sparse parity check matrix. The codes are intituled Gallager coder. Because the computing condition is limited and most people consider that concatenated coder is easy to implement, people ignore Gallager codes little by little. Up to 1995 years, Mackay, Neal and Wiberg rediscovered the merit of Gallager codes and proved its performance can approach Shannon limit. By further research, people bring forward low density parity codes(LDPC codes) with a more widely meaning. In a few years recently, This LDPC codes with more excellent performance will become a new research hotspot in channel error-correcting encoder field. This codes will gain broad application in actual system.This paper gives a research for the basic theory of LDPC codes and its application. The performance of LDPC codes is acquired by computer simulation. This paper mainly include: First, the definition and classify method are introduced. Some useful construction methods are summarized. Then, the encoding algorithms to LDPC codes are provided. The theories of message passing algorithm and belief propagation algorithm are detailed introduced. Whereafter, the performance curves of LDPC codes are received by computer simulation and LDPC codes are applied to the actual system. These include systematic simulation of LDPC codes in image transmission. By simulating, I attain good performance. At last, I propose two ameliorating projects aiming at the application of LDPC codes in image transmission. These two projects include important protection of important image parts using different code ratio and important protection of important image bits using different code length. In the condition of the same systematic performance, these two projects reduce transmission time relay and improve systematic using ratio of frequency band. The finality of paper summarizes my research problem and points out farther research orientation.