H.Garon1,V.Sank1,D.Fisher1,K.Dearth1,J.GalEdd1,A.Ames21NASAGoddardSpaceFlightCenter,Greenbelt,MD207712OrbitalSciences,Gilbert,AZ18April2010

ReportonFlightApplicationSuccessfulUseofaHighRateLDPCCodewithHighDataRateina

RestrictedBandSummary:TheNASAversionoftheLDPC7/8ratecode,shortenedtothedimensionsof(8160,7136),hasbeenimplementedastheforwarderrorcorrection(FEC)schemafortheLandsatDataContinuityMission(LDCM).Thisisthefirstflightapplicationofthiscode.Inordertoplacea440Mspslinkwithinthe375MHzwideXbandwefounditnecessarytoheavilybandpassfilterthesatellitetransmitteroutput.Despitethesignificantamplitudeandphasedistortionsthataccompaniedthespectraltruncation,themissionrequiredBERismaintainedat

Figure1.LDCMEndToEndSoftwareSimulation.

Figure2.BlockdiagramofNASA/GSFCLDCMtestbench.

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concatenatedanLDPCcodewithanouterBCHcodeintendedtoremedypoorlowerrorrateperformance.TheprimaryreasonbehindtheLDCMselectionofLDPC7/8wasbaseduponacombinationofthehighdataraterequirementalongwithalackof(known)errorfloorandavailabilityofflightencodersandgrounddecoders.Still,a7/8ratecodewitha384Mbpsinformationrateleadstoasymbolrateof440Msps.AgoodportionoftheresultingoffsetQPSK(OQPSK)modulationspectrumwhichcouldhavebeentransmittedisinsteadsuppressedbythespacecraft375MHzbandpassfilterinordertosatisfytheDSNspectrallevelrequirement.Theremainingcentralcauseforconcerninestablishinglinkviabilityisthendirectedatassessingtheimpactofthistruncatedspectrumalongwiththerelatedandsubstantialdistortionsonthelinkinbothmagnitudeandphase.LinkSimulation:

Figure3a.Up/Dnconverterdepictedintheblockdiagramoffigure2b.ThereplicaS/Cfilterisatthefarrighthandside.

Figure3b.CharacterizationoftheS/Creplicafilter.

Tomitigatetherisksthatweunderstoodandtobetteranticipatethoserisksstillunknowntous,wesimulatedtheentirelink,endtoend,inbothsoftwareandhardware.Figure1showsthehighlevelblockdiagramcomponentsconstructedinsoftwareusingMathworksSimulinktm.Whiletheblockdiagramshowninfigure2illustratestheoverallfunctionalbreakdownofthehardwarecomponents.ThekeytothehardwaresimulationisanXbandbandpassfilter(figures3aand3b),specificallydesignedtoreplicatethespectrumtruncationanddistortionproducedalongtheanalogportionoftheRFlinkaboardthespacecraft(S/C).InthecaseofLDCMthefilterembodiesthecombinedimpactonthelinkoftheXbandtransmitter,atravelingwavetubeamplifier(TWTA),theDSNbandpassfilterandearthcoverageantenna.Referringtofigure2,inapplyingtheS/Creplicafilteratestmodulatorfirstgeneratesa440MspsPN23datastream,LDPC7/8encoded,at1.2GHz.The1.2GHzoutputofthetestmodulatorisupconvertedto8.2005GHzandthenappliedtotheS/Creplicadistortionfilter.Theoutputofthereplicafilterisdownconvertedbacktoa1.2GHzIFwherebroadbandnoiserepresentativeofthechannelisinjected.Theconsolidatedsignalwithnoiseisfinallypresentedtotheinputofareceiver.ThetestbenchwasintentionallydesignedtoallowtheIFfrequenciesatbothinputandoutputoftheup/downconvertertobeindependentlyvaried.Thelocaloscillatorsoftheup/downconvertercanbeadjustedsothatanycombinationoftestmodulatororgroundreceivercanbeemployedintest.Thelinkspectrumattheinputtothereceiverinsimulation,priortonoiseinjection,isdisplayedinfigure5.Towithintheuncertaintiesofboththehardwareandsoftwaresimulations,thespectrumaspresentedtothereceiverappearsidenticalinbothsoftwareandhardware.

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Figure6.Measuredresults:Minimalimplementationlossbetweenreplicafilterandideal,redandbluerespectively.

Figure5.EmulatedLDCMoutputspectrum, as

ResultsoftheSoftwareSimulationandHardwareEmulation:Usingthehardwaretestbenchasdescribedabove,weareabletodemonstrate(figure6)thata7/8rateLDPCencoded,440Mspsdatastreamcanbefilteredwithabandpassofonly375MHzandstillbedecodedwithaBERoflessthan1012.Moreover,ascanbeseenfromourresults,thishasbeenaccomplishedwithminimalimplementationloss,about1dBforthereceivershownhere,and

equalizationcouldcompensateproperly.Allprogrammablehighdatarate(HDR)receiversusesomeformofequalizationafterconversionoftheanaloginputsignaltodigitalformat.Thegoaloftheequalizationistoproperlyrestorethespreadofbitenergy,theintersymbolinterference(ISI),causebyhardwaredistortions.Somereceiverscapableofcorrectingsignificantandsubstantialmagnitudeandphasedistortiononalinkemploytwostagesofequalization.The1ststageequalizationequatestoamatcheddigitalreceivefilterembeddedwithinaCostasloopofthedemodulatorandbitsynch.The2ndstageAdaptiveBaseBandEqualizer(ABBE)whichfollowsisgenerallydoubleblindandessentiallycompletesamopupactionoftheoutputofthe1ststage.Thelevelofintegrationoftheseequalizerswiththedemodulatorissogreatthatitisdifficulttodistinguishwherethedemodulatorleavesoffandtheequalizersbegin,especiallysinceeachinteractsandimpactsthedemodulatorsodramatically.Theseinitialcoefficientsofboththe1ststageequalizerfilterandtheABBEcanbesetbytheuserandstoredasdefault.Together,bothofthesealgorithmscancompensateforlargeswingsinamplitudeandphaseassumingthattheseoccurwithinsomeconsistencyand,atnottoohigharate.Thereceivercanautomaticallyandcontinuouslyupdatetheadaptiveequalizationstagecoefficientstomaximizeperformance.

Conclusion:CoupledwithacommercialgroundtelemetryreceiverdesignedtodotheLDPCdecodingandtoovercomethelinkdistortions,wehaveabletodemonstratethatwecanmaintainaviable440MspslinkatBERlessthan1012withanimplementationlossoflessthan2dB,despiteanasymmetricaltruncationtoa375MHzbandwidth.TheBERandthegroundimplementationlossarebothextremelylow,inturn,maximizingtheusefulsatellitecontacttime.DuetotheavailabilityofflightencoderchipsqualifiedtoLevel1(GEOenvironment)andtheavailabilityofcommercialreceiverwithdecoders,ithasturnedouttobefortuitousthatLDCMchosetheLDPC7/8ratecodecfortheirnearearthapplication.WiththecontinualpushforevenhigherdatarateswithinanincreasinglymorecrowdedspectrawemayanticipatetheelectionofLDPC7/8asthecodecofchoiceformanymorehighdataratenearearthmissionsinthefuture.

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References:[1]R.G.Gallager,Lowdensityparitycheckcodes,IRETrans.Inform.Theory,vol.IT8,pp.2128,Jan.1962.[2]Y.Kou,S.LinandM.Fossorier,Lowdensityparitycheckcodesbasedonfinitegeometries:arediscoveryandnewresults,IEEETrans.InformationTheory,vol.47,pp.27112736,Nov.2001.[3]W.Fong,WhitePaperforLowDensityParityCheck(LDPC)CodesforCCSDSChannelCodingBlueBook,CCSDSPanel1BMeetingPaper,Sept.2002.[4]G.P.CalzolariandE.Vassalo,CombinedAdvancedCoding&ModulationforFutureCCSDSHighRateMissions,SpaceOps2006,1923June,Rome,taly.