低密度格码编译码原理及其性能仿真

摘要

低密度格码(low density lattice codes,LDLC)是一种崭新的信道编码技术,与LDPC(low density parity check)的译码类似,校验矩阵H都是稀疏的,都通过迭代的消息传递过程来实现其译码,但不同的是:LDPC传递的信息是标量值,而LDLC的信息是(-∞,∞)上的概率密度函数(PDF).当存在高维n的H,且噪声方差σ2＜n(√∣det(H)∣2)∕2πe时,LDLC可以以任意小的误差传输,| det(H)|=1.给出低密度格码的基本原理,并对其编译码算法的实现做详细介绍,最后通过仿真给出其在AWGN信道下的性能.%Abstract: Low density lattice codes (LDLC) are novel channel coding techniques, with similar to LDPC decoding, the check matrix H is sparse and achieving its decoding through passing iterative message; but the difference is that in LDPC codes the messages are scalar values, where for LDLC the messages are probability density function (PDF)over the interval ( -∞, ∞ ) . If and only if there exists a high dimension n of H and σ2 ＜ n√｜ det(H)|2/2πe, LDLC enables transmission with arbitrary small error probability, where σ2 is noise variance and ｜ det(H) ｜ = 1 . In this paper, the basic principles of LDLC are presented, with special emphasis on its encoding and decoding algorithms. Also given are their performance simulation results under AWGN channel.