已阅读5页，还剩38页未读， 继续免费阅读
版权说明：本文档由用户提供并上传，收益归属内容提供方，若内容存在侵权，请进行举报或认领
文档简介
1 YuanLuo Xi anJan 2013 OptimumDistanceProfilesofLinearBlockCodes ShanghaiJiaoTongUniversity HammingDistance CodewordwithLongLengthorShortLength Onewayis Hammingdistance generalizedHammingDistance AnotherDirectionis Hammingdistance distanceprofile Background OurresearchesonODPoflinearblockcode Golay RS RM cycliccodes 3 HammingDistance 4 Although thelinearcodeswithlonglengtharemostoftenappliedinwirelesscommunication thecodeswithshortlengthstillexistinindustry forexample somestoragesystems theTFCIof3G or4G system somedatawithshortlengthbutneedstrongprotection etc CodewordwithLongLengthorShortLength 5 Forthecodeswithshortlength thepreviousclassicboundscanhelpyoudirectly Forthecodeswithlonglength theasymptoticformsofthepreviousclassicboundsstillwork Inthistopic weconsidersomeproblemsinthefieldofHammingdistancewithshortcodewordlength 6 Hammingdistanceisgeneralizedforthedescriptionoftrelliscomplexityoflinearblockcodes DavidForney andforthedescriptionofsecurityproblems VictorWei Wealsogeneralizedtheconcepttoconsidertherelationshipbetweenacodeandasubcode Onewayis Hammingdistance generalizedHammingDistance 7 Inthefollowing weconsidertheHammingdistanceinavariationalsystem Forexample whentheencodinganddecodingdeviceswerealmostselected butthetransmissionratedoesnotneedtobehighinaperiod intheeveningnotsomuchusers seenextslide thenmoreredundanciescanbeborrowedtoimprovethedecodingability Whatshouldwedotorealizethisidea Andwhatistheprinciple AnotherDirectionis Hammingdistance distanceprofile 8 TheTFCIin3Gsystem 9 Details Inlinearcodingtheory whenthenumberofinputbitsincreasesordecreases somebasiscodewordsofthegeneratormatrixwillbeincludedorexcluded respectively 10 Foragivenlinearblockcode weconsider howtoselectageneratormatrixandthen howtoincludeorexcludethebasiscodewordsofthegeneratoronebyone whilekeepingtheminimumdistances ofthegeneratedsubcodes aslargeaspossible BigProblem Ingeneralcase thealgebraicstructuremaybelostinsubcodealthoughthepropertiesoftheoriginalcodearenice Thenhowtodecode 11 12 OneexampleLetCbeabinary 7 4 3 HammingcodewithgeneratormatrixG1 13 ItiseasytocheckthatifweexcludetherowsofG1fromthelasttothefirstonebyone thentheminimumdistances adistanceprofile ofthegeneratedsubcodeswillbe 444 fromlefttoright 14 Andyoucannotdobetter i e byselectingthegeneratormatrixordeletingtherowsonebyoneinanotherway youcannotgetbetterdistanceprofileinadictionaryorder 15 Note wesaythatthesequence3468isbetterthan oranupperboundon thesequence3459indictionaryorder 16 AnotherexampleLetCbethebinary 7 4 3 HammingcodewithgeneratormatrixG2 17 ItiseasytocheckthatifweincludetherowsofG2fromthefirsttothelastonebyone thentheminimumdistances adistanceprofile ofthegeneratedsubcodeswillbe 3337 fromrighttoleft 18 Andyoucannotdobetter i e byselectingthegeneratormatrixoraddingtherowsonebyoneinanotherway youcannotgetbetterdistanceprofileinaninversedictionaryorder Note wesaythatthesequence3689isbetterthan oranupperboundon thesequence3779ininversedictionaryorder 19 MathematicalDescription 2010IT 20 21 Optimumdistanceprofiles 2020 2 4 22 23 TheOptimumDistanceProfilesoftheGolayCodes Forthe 24 12 8 extendedbinaryGolaycode wehave 24 25 Forthe 23 12 7 binaryGolaycode wehave 26 27 Forthe 12 6 6 extendedternaryGolaycode wehave 28 Forthe 11 6 5 ternaryGolaycode wehave 29 FortheresearchesonReedMullercodes seeYanlingChen spaper 2010IT MaybeLDPC inthefuture 30 Todealwiththebigproblem weconsidercycliccodeandcyclicsubcode GOODNEWS Forgenerallinearcode thecorrespondingproblemisnoteasysincefewalgebraicstructuresareleftinitssubcodes Butforcycliccodesandsubcodes itlooksOK 31 GOODNEWS Forgeneralfixedlinearcode thelengthsofallthedistanceprofilesarethesameastherankofthecode Forcyclicsubcodechain thelengthsofthedistanceprofilesarealsothesame 32 GOODNEWS Forgeneralfixedlinearcode thedimensionprofilesarethesame andanydiscussionisundertheconditionofthesamedimensionprofile Itisunluckythat thedimensionprofilesofthecyclicsubcodechainsarenotthesame sowecannotdiscussthedistanceprofilesdirectly Butbyclassifyingthesetofcyclicsubcodechains wecandealwiththeproblem 33 MathematicsDescription 34 ClassificationontheCyclicSubcodeChains 35 1Thelengthofitscyclicsubcodechainsis andJ ms isthenumberoftheminimalpolynomialswithdegreemsinthefactorsofthegeneratorpolynomial 36 2Thenumberofitscyclicsubcodechainsis 3Thenumberofthechainsineachclassis 37 4Thenumberoftheclassesis 5Forthespecialcasen qm 1 wehave whereistheMobiusfunction 38 Example Thenumberofitscyclicsu
温馨提示
- 1. 本站所有资源如无特殊说明，都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等，如果需要附件，请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸，网页内容里面会有图纸预览，若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对用户上传分享的文档内容本身不做任何修改或编辑，并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容，请与我们联系，我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
评论
0/150
提交评论