Matlab-LDPC码性能研究毕业设计说明书

I本科毕业设计（论文）题目LDPC码性能研究II摘要信道编码是数字通信系统的重要组成部分。LDPC信道编码技术是编码界的重要成果之一。1/2码率的二元LDPC码在AWGN信道下的性能距信息理论中的Shannon极限仅差0.0045dB，它是目前距Shannon极限最近的纠错码。Gallagar在1962年提出LDPC码，1996年经过Mackey、Spielman和Wiberg等人的再发现后，LDPC码以其性能优越、全并行迭代译码结构、便于硬件实现等优点，在无线通信、存储工业等领域得到了广泛应用。校验矩阵的构造是编码的前提，本文采用了随机构造法构造，并对矩阵的多种变换方法进行分析，比较了优缺点。译码算法是LDPC码的关键，译码复杂度的大小直接影响系统的实现。主要分硬判决译码、软判决和复合译码。设计中采用的译码方式是软判决译码。在性能分析方面，利用matlab仿真码长、列重和迭代次数对LDPC码性能的影响。仿真结果表明，在一定范围内，LDPC码长码的误码性能优于短码；码长较小时，列重的增加会使性能变差，而对于长码，列重在一定范围内的增大会改善LDPC的误码性能；增加迭代次数会使误码率降低，但当迭代次数大到一定值时，误码率将不会再随着迭代次数的增加而降低。关键词LDPC码信道编码矩阵变换性能分析IIIAbstractChannelcodingisanimportantcomponentfordigitalcommunicationsystems.LDPCchannelcodingtechnologyisoneimportantachievementoftheencodingresults.Theperformanceofhalfofthebinarybit-rateLDPCcodesinAWGNchannelonlyhasatapof0.0045dBtotheShannonLimitthatmakesitbethelatesterror-correctingcodesfromtheShannonLimit.GallagerproposedLDPCcodesin1962,afterMackeyandothersre-discovereditin1996,withbestperformance,completelydecodingalgorithminparallelschemeandeasilyrealizedforhardwaredesign,LDPCcodeshasalreadybeenwidelyusedinmanypracticalsystemssuchaswirelesscommunicationsystemandstoragesystem.TheconstructionoftheCheckmatrixisapreconditionforcoding;therandomizedmethodwasusedinthispaper.Severalwaystotransformthematrixwasdiscussedandbeingcomparedaboutthemeritsofeachmethod.ThedecodingalgorithmisthekeytoLDPCcodeandthecomplexityofdecodingdirectimpactrealizationofthesystem.Therearethreekindsofdecodingalgorithms:hard-decisionmethod,soft-decisionmethodsandhybriddecoding.Thehard-decisionmethodwasusedinthisdesign.BasedonstudyingthebasictheoryofLDPCcodes,theimpactofcodeslength,columnweightanditerationtimesonBERperformanceofLDPCcodesaredemonstratedbycomputersimulationandtheoreticalanalysis.Thesimulationexperimentindicatedthat:LDPCcodeslong-codeerrorperformanceissuperiortoshort-codeerrorperformance,butwhenthecodelengthreachesacertainvalue,andthenincreasethecodelength,BERofLDPCcodeslowerratewillbesmall.Whenthecodelengthissmall,increasingthecolumnweight,LDPCcodesperformancewilldeteriorate;whencodelengthislargeenough,increasingthecolumnweight,LDPCcodesperformancewillbeimproved,butwhenthecolumnweightreachesacertainvalue,assetoutprioritytoincreasingtheperformanceofLDPCcodeswillbeworse.Toincreasethenumberofdecodingiterations,LDPCcodesperformancewillbeimproved;butwhenthenumberofiterationsislargeenough,thenincreasethenumberofiterations,LDPCcodeswillnolongerreducetheerrorrate.keywordsLDPCcodeschannelcodingmatrixtransformationperformanceanalysis目录摘要.....................................................................................................................................IABSTRACT.....................................................................................................................III第1章绪论......................................................................................................................11.1数字通信系统.............................................................................................................11.2信道编码理论及其发展.............................................................................................21.3低密度奇偶校验码的提出、发展和现状.................................................................4第2章预备知识............................................................................................................72.1线性分组码.................................................................................................................72.2信道容量和香农极限...............................................................................................11第3章LDPC码表示及编码....................................................................................143.1LDPC码的定义及其TANNER图表示......................................................................143.1.1LDPC码的定义及其描述.................................................................................143.1.2LDPC码的Tanner图表示................................................................................153.2二进制LDPC码的编码原理...................................................................................163.2.1H矩阵的构造.....................................................................................................163.2.2LDPC码的编码思想......................................................................................17第4章LDPC码的译码思想....................................................................................224.1软判决译码算法.......................................................................................................224.1.1Tanner图解析法原理........................................................................................224.1.2SPA算法原理....................................................................................................244.1.3对数域BP译码算法.........................................................................................274.1.4最小和（Min-Sum）译码算法（改进的对数域BP译码算法）.................294.2硬判决译码算法.......................................................................................................304.2.1Gallager的比特反转译码算法.........