Coded modulation is a bandwidth efficient scheme that combines the functions of coding and modulation. In this contribution, a comparative study of Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM), Bit-Interleaved Coded Modulation (BICM) and Iterative Decoding assisted BICM (BICM-ID) schemes over Gaussian and uncorrelated narrowband Rayleigh fading channels is presented in the context of 8-level Phase Shift Keying (8PSK), 16-level Quadrature Amplitude Modulation (16QAM) and 64QAM. We comparatively study the associated decoding complexity, block length and bandwidth efficiency. It is shown that TTCM constitutes the best compromise scheme, followed by BICM-ID

Hanzo, L.

Liew, T.H.

Ng, S.X.

Yang, L-L.

Italian

Southampton (e-Prints Soton)

COMPARATIVESTUDYOFTCM,TTCM,BICMANDBICM-IDSCHEMESS.X.Ng,T.H.Liew,L-L.Yang,1L.HanzoDept.ofElectronicsandComputerScience,UniversityofSouthampton,SO171BJ,UK.Tel:+44-23-80593125,Fax:+44-23-80594508Email:1lh@ecs.soton.ac.ukhttp://www-mobile.ecs.soton.ac.ukABSTRACTCodedmodulationisabandwidtheÆcientschemethatcombinesthefunctionsofcodingandmodu-lation.Inthiscontribution,acomparativestudyofTrellisCodedModulation(TCM),TurboTrellisCodedModulation(TTCM),Bit-InterleavedCodedModulation(BICM)andIterativeDecodingassistedBICM(BICM-ID)schemesoverGaussianandun-correlatednarrowbandRayleighfadingchannelsispresentedinthecontextof8-levelPhaseShiftKey-ing(8PSK),16-levelQuadratureAmplitudeMod-ulation(16QAM)and64QAM.Wecomparativelystudytheassociateddecodingcomplexity,blocklengthandbandwidtheÆciency.ItisshownthatTTCMconstitutesthebestcompromisescheme,followedbyBICM-ID.1.INTRODUCTIONOneofthemostimportantobjectivesinthedesignofdigi-talcellularsystemsistheeÆcientexploitationoftheavail-ablespectruminordertoaccommodatetheever-increasingtraÆcdemands.Thedesignofcodedmodulationschemesisa￿ectedbyavarietyofcriteria.AhighsquaredFreeEu-clideanDistance(FED)isdesiredforAdditiveWhiteGaus-sianNoise(AWGN)channels,whilehighE￿ectiveCodeLength(ECL)andminimumproductdistancearedesiredforfadingchannels[1].TrellisCodedModulation(TCM)[2]wasproposedorig-inallyforGaussianchannels,whichwasfurtherdevelopedforapplicationsinmobilecommunications[1,3].TurboTrellisCodedModulation(TTCM)[4]isamorerecentjointcodingandmodulationschemethathasastructuresimilartothatofthefamilyofpowereÆcientbinaryturbocodes[5],butemploysTCMschemesascomponentcodes.TTCM[4]requires0:5dBlowerSignal-to-NoiseRatio(SNR)atabiterrorrate(BER)of10￿4,thanbinaryturbocoded8PSKoverAWGNchannels.TCMandTTCMinvokedSet-Partitioning(SP)basedsignallabeling,inordertoachieveahigherFEDbetweentheunprotectedbitsofthecon-stellation,sothatparalleltrellistransitionscanbeassoci-atedwiththeunprotectedInformationBits(IBs).Thisre-ducedthedecodingcomplexity.Furthermore,inourTCMandTTCMinvestigations,randomsymbolinterleaverswereutilised.Anothercodedmodulationschemedistinguishingitselfbyutilisingbit-basedinterleavinginconjunctionwithGraySource TCM/TTCM/BICM EncoderChannelSink TCM/TTCM/BICM DecoderBICM-IDInterleaverInterleaverDeinterleaverModulatorMapper/Demapper/DemodulatorFigure1:Systemoverviewofdi￿erentcodedmodulationschemes.signalconstellationlabelingisreferredtoasBit-InterleavedCodedModulation(BICM)[6].Moreexplicitly,BICMcom-binesconventionalconvolutionalcodeswithseveralinde-pendentbitinterleavers,inordertoincreasetheachievablediversityorder.Withtheaidofbitinterleaversthecode’sdiversityordercanbeincreasedtothebinaryHammingdis-tanceofacode[6].Thenumberofparallelbit-interleaversequalsthenumberofcodedbitsinasymbolfortheBICMschemeproposedin[6].TheperformanceofBICMisbet-terthanthatofTCMoveruncorrelated(orperfectlyin-terleaved)narrowbandRayleighfadingchannels,butworsethanthatofTCMinGaussianchannelsduetothereducedEuclideandistanceofthebit-interleavedscheme[6].Recentlyiterativejointdecodinganddemodulationas-sistedBICMreferredtoasBICM-IDwasproposedin[7,8],whichusesSPbasedsignallabeling.TheapproachofBICM-IDistoincreasetheEuclideandistanceofBICMandhencetoexploitthefulladvantageofbitinterleavingwiththeaidofsoft-decisionfeedbackbasediterativedecoding[8].2.SYSTEMOVERVIEWTheschematicofthecodedmodulationschemesundercon-siderationisshowninFigure1.Thesourcegeneratesran-domIBs,whichareencodedbyoneoftheTCM,TTCMorBICMencoders.Thecodedsequenceisthenappropriatelyinterleavedandusedtomodulatethewaveformsaccordingtothesymbolmappingrules.ForanarrowbandRayleighfadingchannelinconjunctionwithcoherentdetection,therelationshipbetweenthetransmitteddiscretetimesignalxtandthereceiveddiscretetimesignalytisgivenbyyt=￿txt+nt;(1)where￿tistheRayleigh-distributedfadingamplitudehav-inganexpectedvalueofE(￿2t)=1,whilentisthecomplexAWGNwithvariance￿2I=￿2Q=N0=2.ForAWGNchan-nelswehave￿t=1.Thereceiverconsistsofacoherentde-modulatorfollowedbyadeinterleaverandoneoftheTCM,TTCMorBICMdecoders.TTCMschemesconsistoftwocomponentTCMencodersandtwoparalleldecoders.InBICM-IDschemesthedecoderoutputisappropriatelyin-terleavedandfedbacktothedemodulatorinput,asshowninFigure1.Thelog-domainbranchmetricrequiredforthemaximum-likelihooddecodingofTCMandTTCMoverfadingchan-nelsis￿t=jyt￿￿txtj2;(2)whereasthecorrespondingbranchmetricforBICMandBICM-IDisformedbysummingthedeinterleavedbitmet-rics￿ofeachcodedbitvit,yielding￿t=m+1Xi=1￿(vit=b);(3)whereiisthebitpositionofthecodedbitinaconstellationsymbol,misthenumberofIBspersymbolandb2(0;1).Thenumberofcodedbitspersymbolis(m+1),sincethecodedmodulationschemesaddoneparitybittothemIBsbydoublingtheoriginalconstellationsize,inordertomaintainthesamespectraleÆciencyofmbits/s/Hz.TheBICMbitmetrics~￿beforethedeinterleaverarede￿nedas[7]~￿(vit=b)￿minjyt￿￿txj2;x2￿(i;b)(4)where￿(i;b)isthesignalset,forwhichbitiofthesymbolhasabinaryvalueb.TheaveragebiterrorprobabilityofTCMusingMPSK[2]overRicianchannelsathighSNRisgivenby[1]Pb￿=1BC￿(1+K)e￿KEs=N0￿L;Es=N0￿K;(5)whereCisaconstantthatdependsonthedistancestruc-tureofthecode,Bisthenumberofbitsinthetransmissionblock,whileKistheRicianfadingparameter.Further-more,Listheso-calledshortesterroreventpath,i.e.theECLortheminimumsymbolHammingdistancebetweenthetransmittedandreceivedsequence.Finally,Es=N0isthechannel’ssymbolenergytonoisespectraldensityratio.ItisclearfromEquation5thatPbvariesinverselypropor-tionallywith(Es=N0)Landthisratiocanbeincreasedbytimeandspacediversity[1].Diversitymaybeobtainedbyrepetitioncoding(whichreducesthee￿ectivedatarate),space-timecodedmultipletransmitter/receiverstructures(whichincreasescostandcomplexity)orbysimpleinter-leaving(whichinduceslatency).ThecodedmodulationschemesthatwecomparativelystudiedareUngerboeck’sTCM[2],Robertson’sTTCM[4],Zehavi’sBICM[6]andLi’sBICM-ID[8].Table1showsthegeneratorpolynomialsfortheTCMandTTCMcodesinoctalformat.ThesearesystematiccodesthataddoneparitybittotheIBs.Hence,thecodingratefora2m+1-arysignalinPSKorQAMisR=mm+1.ThenumberofRateState~mH0H1H2H32/382110204-(8PSK)64*21033066-3/48311020410(16QAM)64*31011664-5/682110204-(64QAM)64*21011664-Table1:\Punctured"TCMcodeswithbestminimumdis-tanceforPSKandQAM,c￿RobertsonandW￿orz[4].’*’indicatesUngerboeck’sTCMcodes[2].Two-dimensional(2D)modulationisutilised.Octalformatisusedtorep-resentthegeneratorpolynomialsHiand~mdenotesthenumberofcodedIBs.decodingstatesforacodeofmemoryKis2K.WhenthenumberofprotectedIBs~mislessthanthetotalnumberoforiginalIBsm,thereare(m￿~m)uncodedIBsand2m￿~mparalleltransitionsinthetrellisofthecode.Paralleltran-sitionsassistinreducingthedecodingcomplexityandthememoryrequired.RateStateg1g2g3g4dfree2/38426-4(8PSK)(M=3)147-16714-5(M=4)257-6415615-7(M=6)61517-3/4844444(16QAM)(M=3)062402553262265(M=5)16070255RateStateg1g2Puncturingdfree5/681517100103(64QAM)(M=3)0111164133171111113(M=6)10000Table2:ToptableshowsthegeneratorpolynomialsofPaaske’scode,page331of[9].BottomtableshowsthoseoftheRate-CompatiblePunctureConvolutionalcodes[10].MisthecodememoryanddfreeisthefreeHammingdis-tance.OctalformatisusedforthepolynomialcoeÆcientsgi,while’1’and’0’inthepuncturingmatrixindicatethepositionoftheunpuncturedandpuncturedcodedbits,re-spectively.Table2showsthegeneratorpolynomialsfortheBICMandBICM-IDcodesinoctalformat.Thesecodesarenon-systematicconvolutionalcodeshavingmaximumfreeHam-mingdistance.Again,onlyoneextrabitisaddedtotheIBs.Hence,thecodingrateandthespectraleÆciencyaresimilartothatofTCMandTTCMforthe2m+1-arymod-ulationschemesused.Inordertoreducetherequiredde-codingmemory,theBICMandBICM-IDschemesbasedon64QAMwereobtainedbypuncturingtherate-1/2codesfollowingtheapproachof[10].SoftdecisiontrellisdecodingutilizingtheLog-MaximumAPosteriori(Log-MAP)algorithm[11]wasinvokedforthedecodingofthecodedmodulationschemes.TheLog-MAPalgorithmisanumericallystableversionoftheMAPalgo-rithmoperatinginthelog-domain,inordertoreduceitscomplexityandtomitigatethenumericalproblemsassoci-atedwiththeMAPalgorithm[12].3.SIMULATIONRESULTSANDDISCUSSIONSInthissectionwestudytheperformanceofTCM,TTCM,BICMandBICM-IDusingcomputersimulations.Thecom-plexityofthecodedmodulationschemesiscomparedintermsofthenumberofdecodingstatesandthenumberofdecodingiterations.ForaTCMorBICMcodeofmem-oryM,thecorrespondingcomplexityisproportionaltothenumberofdecodingstatesS=2M.SinceTTCMschemesinvoketwocomponentTCMcodes,aTTCMcodeinvokingtiterationsandusinganS-statecomponentcodeexhibitsacomplexityproportionalto2￿t￿Sort￿2M+1.AsforBICM-IDschemes,onlyonedecoderisusedbutthedemodulatorisinvokedineachdecodingiteration.However,thecom-plexityofthedemodulatorisassumedtobeinsigni￿cantcomparedtothatofthedecoder.Hence,aBICM-IDcodewithtiterationsusinganS-statecodeexhibitsacomplexityproportionaltot￿Sort￿2M.3.1.AWGNChannels$RSCﬁle: bicmb.gle$ $Date: 2000/06/27$3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0Eb/No(dB)10-52510-42510-32510-22510-125100BERAWGN, 8PSK4000 Bits/Block2000 Bits/Block500 Bits/BlockTTCM, 8-state, 4 iterationsBICM-ID, 16-state, 4 iterationsTCM, 64-stateBICM-ID, 16-state, 1 iterationsAny Bits/BlockTTCMBICM-IDTCMFigure2:E￿ectsofblocklengthontheTCM,TTCMandBICM-IDperformanceinthecontextofan8PSKschemeoverAWGNchannels.Figure2illustratesthee￿ectsofinterleavingblocklengthontheTCM,TTCMandBICM-IDperformanceinan8PSKschemeoverAWGNchannels.Itisclearfromthe￿gurethatahighinterleavingblocklengthisdesiredfortheiterativeTTCMandBICM-IDschemes.Theblocklengthdoesnota￿ecttheBICM-IDperformanceduringthe￿rstiteration,sinceitconstitutesaBICMschemeusingSPbasedpha-sorlabeling.However,ifweconsiderfouriterations,theperformanceimproves,convergingfastertotheError-Free-Feedback(EFF)bound[7]forlargerblocklengths.AtaBERof10￿4a500-bitblocklengthwasabout1dBinferiorinSNRtermsincomparisontothe2000-bitblocklengthinthecontextoftheBICM-IDscheme.Aslightfurtherim-provementwasobtainedforthe4000-bitblocklength.Inotherwords,theadvantageofBICM-IDoverTCMismoresigni￿cantforlargerblocklengths.The8-stateTTCMper-formancealsoimproves,whenusingfouriterations,astheblocklengthisincreased.$RSCﬁle: states-8psk-awgn.gle$ $Date: 2000/06/27$3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0Eb/No(dB)10-52510-42510-32510-22510-125100BERAWGN, 8PSKTTCM, 8-state, 2 iterationsTTCM, 8-state, 4 iterationsBICM-ID, 8-state, 4 iterationsBICM-ID, 16-state, 4 iterationsBICM, 8-stateBICM, 64-stateTCM, 8-stateTCM, 64-stateFigure3:E￿ectsofdecodingcomplexityontheTCM,TTCM,BICMandBICM-IDperformanceinan8PSKschemeoverAWGNchannelsusingablocklengthof4000IBs(2000symbols).Figure3showsthee￿ectsofthedecodingcomplexityontheTCM,TTCM,BICMandBICM-IDschemes’per-formanceinthecontextofan8PSKschemeoverAWGNchannelsusingablocklengthof4000IBs(2000symbols).The64-stateTCM,64-stateBICM,8-stateTTCMusingfouriterationsand16-stateBICM-IDalongwithfourit-erationsexhibitasimilarcomplexity.AtaBERof10￿4,TTCMrequiresabout0:6dBlowerSNRthanBICM-ID,1:6dBlessenergythanTCMand2:5dBlowerSNRthanBICM.Whenthecodingcomplexityisreducedsuchthat8-statecodesareusedintheTCM,BICMandBICM-IDschemes,theircorrespondingperformancebecomesworsethanthatofthe64-statecodes,asshowninFigure3.Inordertobeabletocomparetheassociatedperformancewiththatof8-stateBICM-IDusingfouriterations,8-stateTTCMalongwithtwoiterationsisemployed.ObservethatduetotheinsuÆcientnumberofiterations,TTCMexhibitsonlymarginaladvantageoverBICM-ID.Figure4showstheperformanceofTCM,TTCMandBICM-IDinvoking16QAMoverAWGNchannelsusingablocklengthof6000IBs(2000symbols).Uponcomparing64-stateTCMwith32-stateBICM-IDusingtwoiterations,weobservedthatBICM-IDoutperformsTCM,forEb=N0inexcessof6:8dB.However,8-stateBICM-IDusinganincreasednumberofiterations,suchasfouroreight,out-performsthesimilarcomplexity32-stateBICM-IDemploy-ingtwoiterationsaswellas64-stateTCM.About1:2dBEb=N0gainwasobtainedatBER=10￿4for8-stateBICM-IDusingeightiterationsover64-stateTCMatasimilardecodingcomplexity.Comparing8-stateTTCMusingtwoiterationsand8-stateBICM-IDemployingfouriterationsrevealsthatBICM-IDperformsbetterfortheEb=N0rangeof5:7dBto7dB.Whenthenumberofiterationsisin-$RSCﬁle: ttcm-bicm-f2000-16qam-awgn.gle$ $Date: 2000/06/27$345678Eb/No(dB)10-52510-42510-32510-22510-125100BERAWGN, 16QAM32-state, 2 iterations8-state, 8 iterations8-state, 4 iterationsBICM-IDTTCM, 8-state, 4 iterationsTTCM, 8-state, 2 iterationsTCM, 64-stateBICM-IDFigure4:ComparisonofTCM,TTCMandBICM-IDem-ploying16QAMoverAWGNchannelsusingablocklengthof6000IBs(2000symbols).creasedtofourforTTCMandtoeightforBICM-ID,TTCMexhibitsabetterperformance,asseeninFigure4.$RCSﬁle: ttcm-bicm-f2000-64qam-awgn.gle,v $ $Date: 2000/05/11 13:03:27 $8.5 9.0 9.5 10.0 10.5 11.0 11.5Eb/No (dB)10-52510-42510-32510-22510-125100BERAWGN, 64QAMTCM, 64-stateBICM, 64-stateBICM-ID, 8-state, 8 iterationsTTCM, 8-state, 4 iterations250 symbols/block2000 symbols/blockFigure5:ComparisonofTCM,TTCM,BICMandBICM-IDusing64QAMoverAWGNchannels.DuetotheassociatedSP,theintrasubsetdistanceofTCMandTTCMincreasesdownthepartitiontree.Itwasshownin[4]thatweonlyneedtoencode~m=2outof5IBsinthe64QAM/TTCMfortargetBERsaround10￿5inAWGNchannels.Hencethereare25￿~m=8par-alleltransitionsduetothethreeuncodedIBsinthetrel-lisof64QAM/TTCM.Figure5illustratestheperformanceofTCM,TTCM,BICMandBICM-IDusing64QAMoverAWGNchannels.Whenusingablocklengthof10000IBs(2000symbols),8-stateTTCMwithfouriterationsisthebestcandidate,followedbythesimilarcomplexity8-stateBICM-IDschemeemployingeightiterations.Again,TCMperformsbetterthanBICMinAWGNchannels.Whenablocklengthof1250IBs(250symbols)wasused,bothTTCMandBICM-IDexperiencedaperformancedegrada-tion.ItisalsoseeninFigure5thatBICM-IDperformsclosertoTTCM,whenalongerblocklengthisused.3.2.UncorrelatedNarrowbandRayleighFadingChan-nels$RSCﬁle: ttcm-bicm-f2000-8psk-xfad.gle$ $Date: 2000/06/27$6 7 8 9 10 11 12 13 14Eb/No(dB)10-52510-42510-32510-22510-125100BERRayleigh Fading, 8PSKBICM-ID, 16-state, 4 iterationsTTCM, 8-state, 4 iterationsBICM, 64-stateTCM, 64-stateFigure6:ComparisonofTCM,TTCM,BICMandBICM-IDfor8PSKoveruncorrelatedRayleighfadingchannelsusingablocklengthof4000IBs(2000symbols).TheuncorrelatedRayleighfadingchannelsimpliedus-inganin￿nite-lengthinterleaverovernarrowbandRayleighfadingchannels.Figure6showstheperformanceof64-stateTCM,64-stateBICM,8-stateTTCMusingfourit-erationsand16-stateBICM-IDemployingfouriterationsinan8PSKschemeoveruncorrelatednarrowbandRayleighfadingchannelsforablocklengthof4000IBs(2000sym-bols).Thesefourcodedmodulationschemeshaveasimilarcomplexity.AscanbeseenfromFigure6,TTCMperformsbest,followedbyBICM-ID,BICMandTCM.AtaBERof10￿4,TTCMperformsabout0:7dBbetterthanBICM-ID,2:3dBbetterthanBICMand4:5dBbetterthanTCM.Theerror￿oorofTTCM[4]waslowerthantheassociatedEFFboundofBICM-ID.However,theBERsofTTCMandBICM-IDwereidenticalatEb=N0=7dB.Figure7comparestheperformanceofTCM,TTCMandBICM-IDinvoking16QAMoveruncorrelatednarrow-bandRayleighfadingchannelsusingablocklengthof6000IBs(2000symbols).Observethat32-stateBICM-IDusingtwoiterationsoutperforms64-stateTCMforEb=N0inex-cessof9:6dB.Forthesamecomplexity,the8-stateBICM-IDinvokingeightiterationsoutperforms64-stateTCMbe-yondEb=N0=8:2dB.Similarto8PSK,thecodinggainofBICM-IDoverTCMinthecontextof16QAMismoresigni￿cantovernarrowbandRayleighfadingchannelscom-paredtoAWGNchannels.NeartheEb=N0of11dBthe8-stateBICM-IDapproachestheEFFbound,hence32-stateBICM-IDusingtwoiterationsexhibitsabetterper-formanceduetoitslowerEFFbound.Observealsothat8-stateBICM-IDusingfouriterationsoutperforms8-stateTTCMemployingtwoiterationsintherangeofEb=N0=8:5dBto12:1dB.IncreasingthenumberofiterationsonlymarginallyimprovetheBICM-ID,butresultsinasigni￿-cantgainforTTCM.Theperformanceof8-stateTTCMusingfouriterationsisbetterthanthatof8-stateBICM-$RSCﬁle: ttcm-bicm-f2000-16qam-xfad.gle$ $Date: 2000/06/27$6 7 8 9 10 11 12 13 14 15Eb/No(dB)10-52510-42510-32510-22510-125100BERRayleigh Fading, 16QAM32-state, 2 iterations8-state, 8 iterations8-state, 4 iterationsBICM-IDTTCM, 8-state, 4 iterationsTTCM, 8-state, 2 iterationsTCM, 64-stateFigure7:ComparisonofTCM,TTCMandBICM-IDfor16QAMoveruncorrelatednarrowbandRayleighfadingchannelstransmitting2000symbols/block(6000IBs/block).IDalongwitheightiterationsforEb=N0valuesinexcessof9:6dB.$RCSﬁle: ttcm-bicm-f2000-64qam-xfad.gle,v $ $Date: 2000/05/11 13:03:27 $10 12 14 16 18 20 22Eb/No (dB)10-52510-42510-32510-22510-125100BERRayleigh Fading, 64QAMTCM, 64-stateBICM, 64-stateBICM-ID, 8-state, 8 iterationsTTCM, 8-state, 4 iterations250 symbols/block2000 symbols/blockFigure8:ComparisonofTCM,TTCM,BICMandBICM-IDusing64QAMoveruncorrelatednarrowbandRayleighfadingchannels.Figure8illustratestheperformanceofTCM,TTCM,BICMandBICM-IDinvoking64QAMoveruncorrelatednarrowbandRayleighfadingchannels.Usingablocklengthof10000IBs(2000symbols),64-stateBICMperformsbet-terthan64-stateTCMforEb=N0inexcessof15dB.BICM-IDexhibitsalowererror￿oorthanTTCMinthisscenario,sinceBICM-IDencodesallthe￿veIBswhileTTCMen-codesonlytwoofthesix64QAMbits.Thethreeunpro-tectedIBsofTCMandTTCMrendertheseschemeslessrobusttotheuncorrelatedfadingchannel.Ifweuseabet-terTCMorTTCMcodegeneratorthatencodesallthe￿veIBs,abetterperformanceisexpected.Reducingtheblocklengthfrom2000symbolsto250symbolsresultedinasmalldegradationforTTCM,butyieldedasigni￿cantdegrada-tionforBICM-ID.4.CONCLUSIONInconclusion,atagivencomplexityTCMperformsbet-terthanBICMinAWGNchannels,butworseinuncor-relatednarrowbandRayleighfadingchannels.However,BICM-IDusingsoftdecisionfeedbackoutperformsTCMandBICMoverbothAWGNanduncorrelatednarrowbandRayleighfadingchannelsatthesamedecodingcomplex-ity.TTCMhasshownsuperiorperformanceovertheothercodedmodulationschemesstudied,butexhibitedahighererror￿oorduetotheuncodedIBsoveruncorrelatednar-rowbandRayleighfadingchannels.5.ACKNOWLEDGEMENTSThe￿nancialsupportoftheEuropeanUnionundertheauspicesoftheTRUSTprojectandtheEPSRC,SwindonUKisgratefullyacknowledged.6.REFERENCES[1]D.DivsalarandM.K.Simon,\ThedesignoftrelliscodedMPSKforfadingchannel:Performancecriteria,"IEEETransactionsonCommunications,vol.36,pp.1004-1012,September1988.[2]G.Ungerboeck,\Channelcodingwithmultilevel/Phasesig-nal,"IEEETransactionsonInformationTheory,vol.28,pp.55-66,January1982.[3]D.DivsalarandM.K.Simon,\ThedesignoftrelliscodedMPSKforfadingchannel:Setpartitioningforop-timumcodedesign,"IEEETransactionsonCommunica-tions,vol.36,pp.1013-1021,September1988.[4]P.Robertson,T.W￿orz,\Bandwidth-EÆcientTurboTrellis-CodedModulationUsingPuncturedComponentCodes,"IEEEJournalonSelectedAreasinCommunications,vol.16,pp.206-218,February1998.[5]C.Berrou,A.GlavieuxandP.Thitimajshima,\NearShan-nonLimitError-CorrectingCodingandDecoding:TurboCodes,"inProceedingsofIEEEInternationalConferenceonCommunications,pp.1064-1070,1993.[6]E.Zehavi,\8-PSKtrelliscodesforaRayleighfadingchan-nel,"IEEETransactionsonCommunications,vol.40,pp.873{883,May1992.[7]X.Li,J.A.Ritcey,\Trellis-CodedModulationwithBitInterleavingandIterativeDecoding,"IEEEJournalonSe-lectedAreasinCommunications,vol.17,No.4,April1999.[8]X.Li,J.A.Ritcey,\Bit-interleavedcodedmodulationwithiterativedecodingusingsoftfeedback,"IEEElectronicsLetters,vol.34,No.10,pp.942-943,May1998.[9]S.LinandD.J.Costello,\ErrorControlCoding:Funda-mentalsandApplications,"EnglewoodCli￿s,NJ:Prentice-Hall,1983.[10]L.H.C.Lee,\NewRate-CompatiblePunctureConvolu-tionalCodesforViterbiDecoding,"IEEETransactionsonCommunications,vol.42,pp.3073{3079,December1994.[11]P.Robertson,E.VillebrumandP.Hoeher,\AComparisonofOptimalandSub-OptimalMAPDecodingAlgorithmsOperatinginLogDomain,"inProceedingsoftheInter-nationalConferenceonCommunications,pp.1009{1013,June1995.[12]L.R.Bahl,J.Cocke,F.JelinekandJ.Raviv,\OptimalDecodingofLinearCodesforMinimizingSymbolErrorRate,"IEEETransactionsonInformationTheory,vol.20,pp.284{287,March1974.

Comparative Study of TCM, TTCM, BICM and BICM-ID Schemes

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