Study On Encoding And Decoding Of LDPC Codes

In 1948,Claude E. Shannon published his famous treatise A Mathematical Theory of Communication. This treatise gave out several important principles for designing error correcting codes, showing the right road for the advancement of the error correcting code technique. At present, Low-density parity-check codes has become one of the best coding technology because of its low complexity iterative decoding algorithm and its approximate to the limited channel capacity.Firstly, this thesis introduces LDPC codes including the history, the developing situation, the definition, the structure, the construction of parity check matrix for LDPC codes, the encoding algorithms and the decoding algorithms. On the basis of the existing theory of low-density parity-check codes, its coding and decoding ideas based on the figure model are expatiated systemically. The detailed derivation of the belief propagation(BP) algorithm information updated rules based both on the white Gaussian noise channels and on log-likelihood ratio probability measurements are made. And based on the algorithm mentioned above, some optimized approximate algorithms are given.Secondly, a simulation system is built based in AWGN channel. For LDPC codes whose code length are 100, 1000 and 10000, we make some simulations by BP decoding algorithm. The results show that the performance is better when code length is longer. Meanwhile we also make two other simulations for different LDPC codes using BP decoding algorithm, the first code length is 10000 and the maximum iterations are 18 and 20, while the second code length is 1000 and the maximum iterations are 10 and 20. From the two simulations we conclude that the larger the maximum iteration, the better the performance. When the code length is 1000, we set the maximum iteration to be 20, and the code rates are 1/2 and 1/3, then we execute BP algorithm on the code. The simulation results show that performance is better under lower rate. In this paper, we study the performance about short code under ML and BP decoding algorithm, also about long code under BP, WBF, simplified BP and modified BP algorithm, namely Min-Sum algorithm and modified Min-Sum algorithm. It is shown by simulation results that soft-decoding has great performance improvements compared to the hard-decoding methods. The revised MSA has improvements compared to the MSA and there is the least performance gap between improved Min-Sum algorithms and BP algorithm.Finally, this thesis describes the density evolution of the regular and irregular codes and introduce the design methods for degree distribution under the guidance of density evolution theory.