Research On LDPC Codes And Optimal Design On Rician Channels

LDPC(Low-Density Parity-Check)Codes are a class of linear block codes with sparse check matrix.It was first discoverd by Gallager.The iterative decoding algorithm of LDPC codes based on Tanner graphs is very simple,and the performance is close to the Shannon limit.LDPC codes show great potential in the B3G mobile communication system.The critical technique of LDPC codes is studied in this thesis,and the optimized regular LDPC ensemble using BP decoding algorithm on Rician channels is presented.In this thesis, we consider the construction of kinds of LDPC codes, especially the PEG methods,and calculate the upper limit of girth of regular LDPC oodes. The steps of BP and LLR-BP decoding algorithms are provided.The density evolution theory of LDPC codes is studied, and the mathematical model of uncorrelated Rician fading channels is constructed.We modify the BP decoding algorithm in order to satisfy the symmetry and stability conditions according to the features of Rician channels, simulate the performance of LDPC codes including PEG-LDPC codes on Rician channels.The results show the performance of LDPC codes is very effective on Rician channels.The Shannon limit under different code rate on Rician channels is calculated. Then we present a method for determining the capacity of regular ensemble on Rician channels under BP decoding algorithm based on the density evolution and features of Rician channels,and calculate the capacity of many ensembles with different code rate,find the optiml regular ensemble on Rician channels.At last we simulate the performance and convergence of the algorithm in the thesis using Matlab and C programming,the results prove that the algorithm we present in the thesis is effective.