基于Matlab的循环码的性能研究

基于Matlab的循环码的性能研究摘要循环码是线性分组码中最重要的一种子类，是目前研究得比较成熟的一类码。它的检、纠错能力较强，编码和译码设备并不复杂，而且性能较好，不仅能纠正随机错误，也能纠正突发错误。循环码还有易于实现的特点，很容易用带反馈的移位寄存器实现其硬件。循环码具有许多特殊的代数性质，这些性质有助于按照要求的纠错能力系统地构造这类码，并且简化译码算法，目前发现的大部分线性码与循环码有密切关系正是由于循环码具有码的代数结构清晰、性能较好、编译码简单和易于实现的特点，因此在目前的计算机纠错系统中所使用的线性分组码几乎都是循环码。关键字：循环码；编码；解码；检错；纠错；MatlabPrincipleandApplicationofCyclicCodesAbstractCycliccodeisalinearblockcodeofasub-classofthemostimportant,isthemorematurestudiedaclassofcodes.Itsreview,errorcorrectionability,codinganddecodingequipmentisnotcomplicated,andtheperformanceisbetter,notonlycancorrectrandomerrors,bursterrorscanbecorrected.Cycliccodealsofeatureseasytoimplement,itiseasytousefeedbackshiftregisterswiththehardware.Cycliccodehasmanyspecialalgebraicproperties,thesepropertiescontributetotheerrorcorrectionabilityofthesystemasrequiredtoconstructsuchcodes,andsimplifythedecodingalgorithm,currentlyfoundinmostofthecloselyrelatedlinearcodesandcycliccodespreciselybecausecycliccodeshaveaclearcodeofalgebraicstructure,betterperformance,encodinganddecodingfeaturessimpleandeasytoimplement,sointhepresentcomputersystemusedbytheerror-correctinglinearblockcodesarealmostalwayscycliccodes.Thisreportdetailsthedefinitionofcycliccodesgeneratedbyageneratorpolynomialmatrixandtheprocessofsystem-generatedmatrix,andwriteintheMatlabenvironment,thecyclecodeencoderanddecodertoachievetheencodinganddecodingfunction.Analysisanddiscussionofthiscodeerrorisfound,theabilitytocorrecterrors.Keywords:Cycliccodes;encoding;decoding;errordetection;correction;Matlab目录摘要...............................................................................................................................IAbstract.................................................................................................................................II第一章绪论........................................................................................................................1第二章算法原理..................................................................................................................22.1循环码定义.............................................................................................................22.2循环码的多项式描述..............................................................................................32.3生成多项式及生成矩阵G..............................................................................42.4系统循环码............................................................................................................42.5循环码的编码：......................................................................................................62.6循环码的解码.........................................................................................................72.7循环码检错与纠错能力..........................................................................................8第三章计算机通信与纠错码.............................................................................................93.1计算机通信技术......................................................................................................93.1.1通信的概念..................................................................................................93.1.2通信的发展史简介......................................................................................93.1.3计算机通信介绍........................................................................................103.2纠错码...................................................................................................................113.2.1纠错码.......................................................................................................113.2.2纠错原理...............................................................................................12第四章程序与SIMULINK仿真......................................................................................144.1程序........................................................................................................................144.1.1程序函数介绍..............................................................................................144.1.2各部分程序说明.........................................................................................154.1.3运行结果.....................................................................................................174.2SIMULINK仿真....................................................................................................194.2.1SIMULINK电路图......................................................................................194.2.2模块参数设置..............................................................................................204.2.3仿真波形....................................................................................................214.2.4仿真结果分析.............................................................................................265总结.................................................................................................................................27参考文献........................................................................................................