密度进化及其简化形式

Density evolution and its approximation forms

密度进化方法是分析现代高效纠错编译码渐近性能的新方法。在简要阐述低密度奇偶校验码(LDPC码)及其和积算法的基础上,较系统地论述了密度进化方法的基本原理。该方法在不同信道下有不同的简化形式。针对规则LDPC码详细给出了在AWGN信道下确定其门限值的高斯近似及删除信道近似方法。该方法可操作性强,能在未进行误比特率(BER)仿真的情况下分析码字性能,对高效纠错编译码的优化设计具有重要的指导作用。

Density evolution is a new method for analyzing the asymptotic performance of near capacity limit error-correcting codes. The low-density parity-check codes (LDPC)and sum-product algorithm are introduced first, then the principle of density evolution , which is in different approximation forms over different channels, is discussed systematically. At last, two approximation methods for calculating thresholds over an AWGN channel are given based on regular LDPC. This method is of practicability, and can provide excellent approximate estimation of the encoding and decoding performances without bit error rate(BER) simulation. This is significant for density evolution to optimize near Shannon limit error-correcting codes.