Chapter 10 Error-Control Coding第10章差错控制编码

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1、Chapter10Error-ControlCodingError-ControlCodingistheplatformofShannonchannelcodingtheorem.10.1Introduction©Po-NingChen@cm.nctuChapter10-2110.1IntroductionoErrorcorrectionversuserrordetectionnThereisanalternativesystemapproachtoachievereliabletransmissionotherthanforwarderror

2、correction(FEC).nBythesystemstructure,itisnamedautomatic-repeatrequest(ARQ),whichisacombinationoferrordetectionandnoiselessfeedback.©Po-NingChen@cm.nctuChapter10-310.1IntroductionoClassificationsofARQnARQwithstop-and-waitstrategyoAfterthetransmissionofacodeword,thetransmitte

3、rstopsandwaitsforthefeedbackbeforemovingontothenextblockofmessagebits.nContinuousARQwithpullbackoThetransmittercontinueitstransmissionsuntilaretransmissionrequestisreceived,atwhichpointitstopsandpullsbacktotheincorrectlytransmittedcodeword.nContinuousARQwithselectiverepeatoO

4、nlyretransmitethecodewordsthatareincorrectlytransmitted.©Po-NingChen@cm.nctuChapter10-4210.3Linearblockcodeso“10.2Discretememorylesschannels”hasbeenintroducedinChapter9,soweomitit.oLinearcodenAcodeislinearifanytwocodewordsinthecodecanbeaddedinmodulo-2arithmetictoproduceathir

5、dcodewordinthecode.nThecodewordsofalinearcodecanalwaysbeobtainedthrougha“linear”operationinthesenseofmodulo-2arithmetic.©Po-NingChen@cm.nctuChapter10-510.3LinearblockcodesoForalinearcode,thereexistsak-by-ngeneratormatrixGsuchthatoGeneratormatrixGissaidtobeinthecanonicalformi

6、fitskrowsarelinearlyindependent.©Po-NingChen@cm.nctuChapter10-63Whatwillhappenifonerowislinearlydependentonotherrows?SupposeThen©Po-NingChen@cm.nctuChapter10-7Hence,thenumberofdistinctcodewordsisatmost2k-1(nottheanticipated2k).©Po-NingChen@cm.nctuChapter10-8410.3Linearblockc

7、odesoParity-checkmatrixHnTheparity-checkmatrixofacanonicalgeneratormatrixisan(n-k)-by-nmatrixsatisfyingwherethecolumnsofHarelinearlyindependent.nThen,thecodewords(orerror-freereceptions)shouldsatisfy(n-k)parity-checkequations.©Po-NingChen@cm.nctuChapter10-910.3Linearblockcod

8、esoSyndromesnThereceptionsmaybeerroneous(witherrorpatterne).nWiththehelpofp