Satellite-Communication---7Error---Control

2011/4/[e-mail]7:ErrorControlforDigitalSatelliteLinks1.Knowledge2.ErrorControlCoding4.PerformanceofBlockErrorCorrectionCodes5.ConvolutionalCodes6.ImplementationofErrorDetectiononSatelliteLinks7.ConcatenatedCodingandInterleaving8.TurboCodesSummary1.KnowledgeInanaloglinksDegradation–decreaseinS/NratioUsewidebandFMtoachieveagoodbasebandS/NwithlowC/NIndigitallinksDegradation–measuredinBERUsePSKtoachievegoodBERswithlowC/NFundamentaldifference–analog,digitalsignalsCanimprovethequalitybyusingerrorcorrectiontechniques1.KnowledgeRedundantbits–addedtodatastreamCantellwhenanerroroccursCanpointtotheparticularcorruptedbitorbitsErrordetection-onlydetecterrorsForwarderrorcorrection(FEC)–detectandcorrecterrorsErrorcontrol–whenanerrorisdetected,adecisionmustbemadewhatactiontotake–ignoretheerror,flagtheerror,sendablockofinformationagain,estimatetheerror,replacethecorrupteddata1.KnowledgeCodingAdditionalbitsaddedtothedatastreamtoformanerror-detectingorerror-correctingcodeIntheory,itispossibletogeneratecodescandetectorcorrecteveryerrorinagivendatastreamInpractice,atrade-offbetweenthenumberofredundantbitsandthetransmissionrateEfficiency:measureofthenumberofredundantbits•HalfrateFEC:redundantbits=databits•Lowerrorratetradeforlossofcommunicationcapacity1.KnowledgeChannelcapacityUpperlimitontheinformationcapacityofthechannelforanycommunicationsystemwithanoisychannelAWGNchannel,capacityH•B:channelbandwidthinHz•P:receivedpowerinwatts•N0:singlesidednoisepowerspectraldensityinwattsperHz20log1/()HBPNBbps2011/4/1021.KnowledgeH=1/Tb,Tb:bitdurationEnergyperbitis:E=PTb=P/HEb/N0=P/(HN0)H/B:spectralefficiencyofthecommunicationlink,ratioofbitratetobandwidthofthechannel20log1bEHHbpsBNBRelationshipbetweenH/BandEb/N0forpowerlimited(HB,notusebandwidthefficiently)caseandlowEb/N0ratio.-1.6dBistheShannonbound–setsalowertheoreticallimitontheEb/N0canbeusedincommunicationlink.RegardlessofthemodulationorcodingschemesTurbocodesallowlinkstooperatedowntoC/Nratiosof0dBatacceptableBERRelationshipbetweenH/BandEb/N0forbandwidthlimited(HB,capacitycanbeincreasedbyusingavailabletransmitterpowerinawiderbandwidth))casehighEb/N0ratio.Coding,especiallyFEC–improvethelinkperformanceunderconditionsoflowC/N,withoutincreasingthebandwidth2.ErrorControlCodingErrordetectioncodingAddingredundantbitstoadatastreamOneredundantbitisaddedforeveryNdatabits–allowsasingleerrorwithinthatblockofNbitstobedetected,NisarbitrarySinglebitparityappliedto7–bitASCIIcode•7–bitASCIIcode–consistsof128characters•Eighthbit–paritybit,usedfordetectionoferrorinthe7bits(a)Exampleofevenandoddparityfora7-bitASCIIword.(b)Exampleoferrordetectionina7-bitASCIIwordwithevenparity.Errorbitsareunderlined.Errorratep:single-biterrorprobabilityn:numberoftotalbitstransmittedk:numberofbitsbeingerrorFor7-bitASCIIcharacters,oneparitybitisaddedtodetectoneerror,7databits.ProbabilityofanundetectederroroccuringinanASCIIwordisPwcpc:single-biterrorfor8-bitword()(1)knkenPkppk2628(2)(2)(1)282wcecccPPppp2011/4/103Withoutparity,probabilityPwuofasingleerrorinthe7bitwordisWecansee,theimprovementinrateofundetectederrorsforASCIIwordsis4pcAboveexampleillustrateshowpowerfulevenasingleparitybitcanbeinthedetectionofbiterrorsinalinkwithlowBER67(1)71wucccPpppBlockerrordetectionTransmitdataasblocks(n,k)-nbitsinablock,madeupofkmessagebits+rparitybitsn=k+rLinearblockcodes2ncodewords,kmessagebits,(n-k)redundantcheckbitsSystematiclinearblockcode:firstkbits–message,remaining(n-k)bits–paritybits.GeneralfromofalinearcodewordCC=DGD:k-bitmessageG:generatormatrixtocreatetheparitycheckbitsfromdatabits2kvalidcodewordswithin2ncodewordsDefinitionofcapabilitiesoflinearblockcodeWeightw:numberofnonzerocomponentsofCDistanced:numberofcomponentsforC1andC2differ•E.g.,C1=011011;C2=110001;d(C1,C2)=3Minimumdistancedmin:smallestdistancebetweenanypairsofcodewordsintheentirecodeErrordetectioncodeNumberoferrorscanbedetectedindmin-1Numberoferrorscanbecorrectedis(dmin-1)/2CycliccodeDefinition:An(n,k)linearcodeCiscalledacycliccodeifeverycyclicshiftofacodevectorinCisalsoacodevector.Forcycliccodes,avalidcodeword(c0,c1,…,cn-1),shiftedrightonebit,isalsoavalidcodeword(cn-1,c0,…,cn-2)Examples:Hammingcodes,GolayCodes,BCHcodes,RScodesHammingcodesHammingcodesDesignedtocorrectsinglebiterrorsGeneratormatrixGParity-checkmatrixHHowtoconstructG?[7,4]binaryHammingCode2011/4/104A=[a6，a5，a4，a3，a2，a1，a0]isthetransmittedcodeworda2，a1，a0areparitybitsa6，a5，a4，a3aremessagebitsThreelinearindependentequationswhichcangenerateallofthe(7,4)Hammingcodewords•a2=a6+a5+a4•a1=a6+a5+a3•a0=a6+a4+a3Allof(7,4)codewords00000000810001111000101191001100200101011010100103001111011101100140100110121100001501011011311010106011001114111010070111000151111111a6a5a4a3a2a1a0a6a5a4a3a2a1a0MinimalHammingdistanceis3Accordingtothelinearequations,wehaveHisparity-checkmatrix311101001101010[]1011001HPI6543210111010001101010010110010Taa