基于下三角H矩阵的LDLC整形研究文章编号：10019081(2013)07183603doi: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0.31dBo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Shapingmethodfor1owdensitylatticecodesbasedonlowertriangularmatrix英文作者名ChongqingKeyLaboratoryofSignalandInformationProcessing,ChongqingUniversityof卩ostsandTe1ecommunications,Chongqing400065,China英文摘要)Abstract：TosolvetheproblemthatLowDensityLatticeCodes(LDLC)cannotbeusedontheconstrainedpowercommunicationAdditiveWhiteGauss-ianNoise(AWGN)channel,theshapingmethodswerestudied.Tnthispaper,a1owertriangularHmatrixwithaspecialstructurewascon-structedfirst,togetherwiththehypercubeandsystematicshapingmethod,andthentheaveragepowerwasfixed,thepositionchangeoflatticepointbeforeandaftertheshapingprocess,anditscorre-spondingshapinggainwereanalyzed.TheSimulationresultsshowthatthecodewordisuniformlydistributedwithintheVoronoiregionsofthelatticeaftershaping,andtheseshapingmethodscanachieveashapinggainof1.31dBwhenSymbolErrorRate(SER)10-5andcode1ength10000whichimprovesOe31dBcomparedwiththetraditionalshapingtechnique.Powerlim-itedlatticepointsweregeneratedefficientlyaftershaping・TosolvetheproblemthatLowDensityLatticeCodes(LDLC)cannotuseontheconstrainedpowercommunicationAdditiveWhiteGauss-ianNoise(AWGN)channel,shapingmethodswasstudied.Inthispaper,alowertriangularHmatrixwithaspecialstructurewasconstructedfirst,togetherwiththehypercubeandsystematicshapingmethod,andthentheaveragepowerwasfixed,thepositionchangeoflatticepointbeforeandaftertheshapingprocess,anditscorrespondingshapinggainwereanalyzed.ThesimulationresultsshowthatthecodewordisuniformlydistributedwithintheVoronoiregionsofthelatticeaftershaping,andtheseshapingmethodscanachieveashap-inggainof1.31dBwhenSER10-5andcodelength10000whichimproves0.31dBcomparedwiththetraditionalshapingtechnique.Powerlimitedlatticepointswasgeneratedefficientlyaftershaping・英文关键词Keywords:LowDensityLatticeCodes(LDLC);latticepoint;hypercubeshaping;systematicshaping0引言格码(latticecodes)可以看作是类似线性二进制码字的欧氏空I'可,能够达到加性高斯白噪声(AdditiveWhiteGaussianNoise,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Som-mer等提出了低密度格码(LowDensityLatticeCodes,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二10000、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]o因此，LDLC在AWGN信道上及在多入多出(MultipleInputMultipleOutput,MIM0)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，IDLC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。