Rice信道下LDPC码密度进化的研究

应用低密度奇偶校验(LDPC)码译码消息的密度进化可以得到码集的噪声门限，依此评价不同译码算法的性能，并可以用来优化非正则LDPC码的次数分布对。该文首先以Rice信道下正则LDPC码为例，讨论了不同量化阶数及步长时BP，BP-based 和offset BP-based 3种译码算法的DDE(Discrete Density Evolution)分析，接着在offset BP-based译码算法的DDE分析基础上，采用差分进化方法对Rice信道下非正则LDPC码的次数分布对进行了优化，得出了相应的噪声门限。最后，给出了Rice信道下码率为1/2的优化非正则LDPC码的概率聚集函数(PMF)进化曲线。

Research of Density Evolution of LDPC Codes over Rice Channels

Noise threshold of Low Density Parity Check (LDPC) codes ensemble could be calculated by density evolution of the decoding messages. According to the threshold, performance of the decoding algorithm could be evaluated and degree distribution pairs of irregular LDPC codes also might be optimized. In this paper, for regular LDPC codes on Rice channel, DDE for BP,BP-based and offset BP-based decoding algorithm were compared on different quantization level and step. Furthermore, degree distribution pairs of the irregular LDPC codes were optimized on Rice channel, which was based on DDE for offset BP-based decoding algorithm, the corresponding threshold is also calculated. Finally, the Probability Mass Function (PMF) evolution curve of optimized irregular LDPC codes with code rate 1/2 on Rice channel is given.