Study On Parity-Check Matrix Construction And Encoding Of LDPC Codes

In recent years, wireless communication is developing very fast. The third generation (3G) of mobile communication technology had been put into business applications and more researches about fourth generation (4G) of mobile communication are still needed to be done. The complexity of wireless environment and the finites of wireless resources need the communication systems must satisfy both the reliability of the signals and bandwidth efficiency. According to Shannon Information Theory, channel coding is the crucial technology for ensuring the reliability of information transmission.Low Density Parity Check code is a kind of good codes, which was first invented by R. Gallager in 1962. In late 1990s, D. J. C. Mackay and R. M. Neal rediscovered LDPC code, and they brought Belief-Propagation (BP) algorithm into the decoding of LDPC codes and got the excellent performance achieving up to Shannon Limit. The outstanding performance of LDPC code comes from the special structure of parity check matrix and the iterative decoding algorithm. This thesis investigates the construction of parity check matrix and encoding algorithm of LDPC code.From the view of Shannon Information Theory, gives a systematic review on the development of channel coding theory and LDPC code, introduces basic knowledge of LDPC on graphs. Mainly introduces several typical decoding algorithms and optimization and analysis tools of LDPC code.The following section introduces several structured construction methods, including finite geometry method, circulant matrix method andπrotation LDPC code. Focuses onπrotation LDPC codes, and gives simulation results.The encoding of LDPC codes constructed by structured methods is very easy and flexible, but there exists a gap between the performance of these LDPC codes and the performance of LDPC codes constructed by random algorithms. So introduces several random construction algorithms and linear-time-encoding algorithm. Research focuses on Progressive-Edge-Progress PEG algorithm, and proposes an improved PEG algorithm which can construct lower or almost lower triangular parity matrix suitable for linear-time-encoding. Compared with Xiaoyu Hu's original improvement, this new algorithm can be applied to any symbol degree distribution pair and also regular codes.Simulation results show, the performance of the LDPC codes constructed by algorithm proposed by this thesis is as excellent as the original PEG algorithm. Due to the limit of binary LDPC codes, have a discussion on the construction of Qary-LDPC codes using PEG method. And the improved PEG algorithm proposed by this thesis is also suitable for constructiong Qray parity-check matrix for linear-time-encoding.Gives corresponding decoding algorithm. Simulation shows that the performance of Qary-LDPC codes is improved with the increase of the order of finite field.