【作者】 杨超；

【导师】 孙蓉；

【作者基本信息】 西安电子科技大学 ， 通信与信息系统， 2014， 硕士

【摘要】 1948年香农发表了《通信的数学理论》,其中给出了设计纠错码的几个基本原则,为纠错码技术的发展指明了方向。目前,LDPC码以其低复杂度的迭代译码算法和可逼近信道容量限而成为目前最佳的编码技术之一。首先,本文介绍了LDPC码的历史、发展现状、定义、结构、校验矩阵构造方法、编译码算法,在对LDPC码现有理论研究的基础上,系统地分析和总结了LDPC码基于图模型的编译码思想。详细推导了LDPC码在高斯白噪声信道下的置信传播译码算法的消息更新规则,给出了基于对数似然比概率测度下的置信传播算法的消息更新规则,并针对此种算法给出了几个优化近似的算法。其次,应用MATLAB软件构建了加性高斯白噪声信道下的性能仿真系统。仿真码长分别为100、1000、10000,译码算法采取LLR BP算法的LDPC码误码性能,从仿真结果可以得知码长越长其误码性能越好;仿真码长为10000,译码算法采取LLR BP算法的LDPC码分别在最大迭代次数为18、20下的性能曲线,和码长为1000的LDPC码分别在最大迭代次数为10、20下的性能曲线,从仿真结果可以看出,一定条件下最大迭代次数越大,误码性能越好;仿真码长为1000,最大迭代次数为20次,码率分别为1/2和1/3的LDPC码误码性能曲线,从仿真结果可以得出低码率要比高码率的性能好;分别仿真短码情况下最大似然译码和BP译码算法的误码性能曲线,长码情况下BP算法和WBF算法的误码性能曲线,简化的BP算法LLR BP算法的性能曲线,以及改进的BP算法——最小和算法和改进的最小和算法性能曲线。从仿真结果得到,软判决译码算法较之于硬判决译码算法,误码率性能有明显增益,改进的最小和算法较之于最小和译码算法,误码率性能增益明显,并且改进的最小和算法和BP算法性能差异较小。最后,分别介绍了规则码和非规则码的密度进化,并详细讨论研究了密度进化理论指导的度序列分布的优化设计方法。更多还原

【Abstract】 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.更多还原