基于下三角H矩阵的LDLC整形研究
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文章编号:10019081(2013)07183603
doi:10.11772/j.issn.10019081.2013.07.1836
摘 要：
针对低密度格码(LDLC)编码后不能适应在功率限制的加性高斯白噪声(AWGN)信道上传输的问题，研究了编码前的整形问题。构造了一种特殊结构的下三角H矩阵，并结合超立方整形和系统整形方案，分析并仿真了整形前后格点的变化及取得的整形增益。结果显示：整形后的码字沿格的Voronoi域均匀分布，并当码长为10000、误码率为10-5时，可得到1.31dB的整形增益，相对于传统的整形技术提高了0.31dB。通过整形，有效地产生了功率受限的格点。
关键词：低密度格码；格点；超立方整形；系统整形
中图分类号：TN911.22
文献标志码:A
英文标题
Shaping method for lowdensity lattice codes based on lower triangular matrix
英文作者名
ZHU Lianxiang, LUO Hongyu*
英文地址(
Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
英文摘要)
Abstract：
To solve the problem that Low Density Lattice Codes (ldlc) cannot be used on the constrained power communication Additive White Gaussian Noise (AWGN) channel, the shaping methods were studied. In this paper, a lower triangular H matrix with a special structure was constructed first, together with the hypercube and systematic shaping method, and then the average power was fixed, the position change of lattice point before and after the shaping process, and its corresponding shaping gain were analyzed. The simulation results show that the codeword is uniformly distributed within the Voronoi regions of the lattice after shaping, and these shaping methods can achieve a shaping gain of 1.31dB when Symbol Error Rate (SER) 10-5 and code length 10000 which improves 0.31dB compared with the traditional shaping technique. Power limited lattice points were generated efficiently after shaping.
To solve the problem that Low Density Lattice Codes (LDLC) can not use on the constrained power communication Additive White Gaussian Noise (AWGN) channel, shaping methods was studied. In this paper, a lower triangular H matrix with a special structure was constructed first, together with the hypercube and systematic shaping method, and then the average power was fixed, the position change of lattice point before and after the shaping process, and its corresponding shaping gain were analyzed. The simulation results show that the codeword is uniformly distributed within the Voronoi regions of the lattice after shaping, and these shaping methods can achieve a shaping gain of 1.31dB when SER 10-5 and code length 10000 which improves 0.31dB compared with the traditional shaping technique. Power limited lattice points was generated efficiently after shaping.
英文关键词Key words:
Low Density Lattice Codes (LDLC); lattice point; hypercube shaping; systematic shaping
0 引言
格码(lattice codes)可以看作是类似线性二进制码字的欧氏空间，能够达到加性高斯白噪声(Additive White Gaussian Noise，AWGN)信道的信道容量［1］，它提供了一个连续字符的编码方法，将整数值信息比特转化为欧氏空间的格点,可以看作是无限星座点在欧氏空间的子集。2007年 Sommer等提出了低密度格码(Low Density Lattice Codes, LDLC)［2］，它是一种切实可行的、可达到信道容量的格码。近年来，许多学者都对LDLC进行了相关研究，并证明当码长为n=10000、误码率为10-5时，LDLC距离信道容量仅0.8dB，其译码器具有较低的复杂度［3-5］。因此，LDLC在AWGN信道上及在多入多出(MultipleInput MultipleOutput, MIMO)通信系统中都具有极大的潜力。
目前LDLC的研究主要围绕编译码算法及H矩阵的构造展开［6-7］，然而为了满足功率受限的条件，LDLC编码前需要进行整形处理。最优的整形方案是将码字映射到球形的整形区域内，以使每个码字都能服从高斯分布，在理论上这可以实现1.53dB的整形增益［8］，然而实际操作中却难以实现。所以，一般地是将码字映射到有限的星座图上，使最终传输的信号在每个星座点上都能均匀分布。