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Department of Electrical & Computer Engineering
ELEC 691X/498X – Broadcast Signal TransmissionFall 2015
Instructor:DR.RezaSoleymani,Office:EV‐5.125,Telephone:848‐2424ext.:4103.OfficeHours:Wednesday,Thursday,14:00– 15:00Time:Tuesday,2:45to5:30Room: H411
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Department of Electrical & Computer Engineering
Inthislecturewecoverthefollowingtopics:
• ErrorControlCoding:FECversusARQ.• BlockandConvolutionalCodes.• ReedSolomon RS Codes.• ConcatenatedCodingusedinDVB‐T.
Possiblyinthefuturelectures:
• LowDensityParityCheck LDPC CodesinDVB‐S2.• RaptorCodes.
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Department of Electrical & Computer Engineering
Inpreviouslectures,wehavelearntaboutdatacompression,i.e.,howtoencodethevideowiththeleastpossiblebitrategivenadesiredlevelofquality.Wehavealsolearnthowtopacketize,i.e.,organizingthebitsattheoutputoftheencoderintostreamofequallengthpackets:TransportStream MPEG‐TS .Thesepacketsarethensentoverthechanneltothereceiversothattheycanbedecodedandusedbytheclient.Alternatively,thepacketizedstream TS canbesavedonastoragemediumsuchasaDVDoraBlu‐raydiskforfutureviewing.Datagoingthroughanymediumencounternoiseandotherimpairmentsresultinginerrorsinthetransportstream.IntheanalogTVorincasewecouldencodethevideopixelbypixel,theeffectofnoisewouldbelimitedtoonepixel.However,inthecaseofMPEGencoding,anerrormayresultindestroyingseveralmacroblocksorevenGroupofPictures GOP resultingindestroyingconsiderablepartofavideo.EvenasingleerroneousbitmaycauseeffectsthatmaypersistuntilthearrivalofanewIntra‐frame I‐frame orevenlonger.Iferrorrateincreases,thepictureis
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completelylost.Whileintheoldanalogsystem,theeffectofnoisewasseendirectlyassnowflakelikeimpairmentinthepictureandtheeffectofnoiseincreasedasafunctionofthequalityofyourreceiverthenoisepowerandyourdistancefromtheTVstation yourreceivedpower inacontinuous graceful way,inthecaseofdigitalTV,youeitherhaveperfectpictureornothing.
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Department of Electrical & Computer Engineering
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Department of Electrical & Computer Engineering
InTerrestrialTV DVB‐T/T2 orsatelliteTV DVB‐S/S2/S2X transportstreamistransmitteddirectly,weonlyneedtoconcernourselveswithbiterrorsanduseerrorcorrectingcodesatthephysicallevel.However,withtheincreaseinthenumberofviewerswatchingTVovertheInterneteitherIP‐TVorOTTapplicationssuchasNetFlix,TSismoreandmorebeingtransmittedoverIP.Thatis,MPEGTransportStreamsgetencapsulatedinsideanIPstream.WiththeincreaseinthespeedoftheInternetwhetheritisthelandline cableandVDSL orwirelesssuchasLTE,real‐timebroadcastingofvideoovertheInternethasbecomefeasible.GoingoveranIPnetwork,anMPEG‐TSfacesanothertypeofdatalossduetolossofthepacketsasaresultofcollisionand/bufferoverflow.Toovercomethistypeoftransmissionimpairment,weneedtouseerrororpossiblyerasureprotectioncodingatthetransportandhigherlayers.
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Department of Electrical & Computer Engineering
Real‐timetransportprotocol
IPnetworkswerenotdesignedforreal‐timedeliveryofdataandcanhaveunpredictablejitteranddelay.TomaintainQoS,themultimediadatathattravelsontheIPnetworksmustarriveontimeandinthesameorderitwassent.Real‐timeTransportProtocol RTP canbeusedtoaddressthetime‐criticalrequirementofmultimediabitstreams.RTPprovidesatimestampandsequencenumbertoIPpacketscontainingmediadata.Thesecanbeusedbythereceivertosynchronizeplaybackandmanagebuffersminimizingnetworkjitter.
EncapsulatingmediadataintoIPpackets
DeliveringmediabitstreamsoverIPrequiresseverallayersofencapsulation.MPEG‐2transportstreams,forexample,consistofaseriesof188‐bytepackets.Thesearegroupedtogetherandwrappedwithinan
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RTPpacket.Finally,theRTPpacketisencapsulatedwithinaTCPorUDPdatagram,forminganIPpacket.FigurebelowshowsanRTPpacketcontainingseveralMPEG‐2transportpacketswithinitspayload,allencapsulatedusingUDPinanIPpacket.Thisdiagramshowsseven188‐bytetransportpacketsthatconstitutetheRTPpayload.Eachencapsulationaddsadditionalheaderdataandaddstothetotalrequiredbandwidth.
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Department of Electrical & Computer Engineering
IfthenetworkhassufficientQoS,itispossibletodelivermediapacketswithouttheoverheadofRTP.ThepacketsareinsteadinserteddirectlyintoUDPpackets.NextfigureshowshowMPEG‐2transportstreampacketscanbeencapsulatedwithinaUDP/IPpacket.
SendingMPEG‐2transportstreampacketsoverUDPisusedextensivelywithintheprivatenetworksofcableandtelephonecompaniestodeliverMPEG‐2transportstreamsthroughoutthesystem.ForgeneraldeliveryovertheunmanagedInternetwithoutQoS guarantees,streamingprotocolssuchasRTPmaybeused,buteventhen,packetsmaybelostindelivery,resultinginartifactsinthemediapresentation.
TCP:TransmissionControlProtocol.UDP:UserDatagramProtocol.RTP:Real‐timeTransportProtocol.
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Inordertoperformerrordetection/correction,weneedtoaddoverheadtothedatatobetransmittedinordertomakealegitimatedatastreamdifferentfromarandomlycorruptedstreamofdata.Theoverheadwillbeintheformofparities.Asanexampleconsidertransmissionofanumber ofbits.Thebitsinakbitlongmessagerepresentvaluesrangingfrom0to2 1 forexampleifk 8,thenumbersrangefrom0to255.Nowifabitisinerror,wegetanotherdatastreamwhichisinourlistandwedonotnoticetheerror.Now,ifweaddonextrabitsuchthatthenumberof1’sinthestreamisodd oreven thenasingleerrorwillchangetheparityandwewillgetapatternwhichweknowcouldnothavebeentransmitted.So,wedetectasingleerrorbyaddingasingleparitybit.Wemayfindthelocationoftheerroraswellifweaddseveralparitybitseachmakingtheparityofasubsetofthebits.Example: Considerthatwehavea4bitlongmessage, , , , .Ifweaddthreeparitybits, , , suchthat,
⊕ ⊕
⊕ ⊕
⊕ ⊕
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Thenanerrorin willresultinparities and beingviolatedandanerrorinin willresultinparities and beingchangedandsoon.Thisisa 7,4 Hammingcodethatcancorrectanysingleerror.Notethatherewehaveincreasedtherateoftransmissionand,therefore,therequiredbandwidthby7/4inordertoprotectbitsfrombeingdeliverederroneously.Let’snowaccesstheperformanceofthissimplecode.Assumethatwehadan of
10dB. Thatis 10 10.AssumeweareusingQPSKmodulationwhere
2 4.47 3.9 10 .Ifweusetheabove 7,4 code,for
each4bitswesend7bits.So,inordertokeep constant,weneedtoreducethe
energypereachcodedbitby4/7.Thismeansthatwetransmitatan of
10 5.71.Thebiterrorratebeforeerrorcorrectionwillbe 2 5.713.38 3.62 10 .Buttheprobabilityoferrorafterdecodingisthe
probabilitythatwehavemorethanoneerrorattheoutputofthedemodulatorbeforethedecoding .
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Theprobabilityofanerroristhen,
1 0 1
or,1 1 7 1
wherep 3.62 10 and,therefore, 2.75 10 .Assumingthatwhenthereisanerrorina7bitcodeword ontheaveragehalfthebitsareinerror,thebiterrorrateofthecodedsystemis1.37 10 whichisroughlythesameastheun‐codedsystem.Thereasonforthepoorperformanceofthecodeisitsshortlength.Hammingcodesmaybedesignedofanylength 2 1andinformationlength 2 1 foranyinteger 2.Thenumberofparitybitsis andtheycanallcorrectoneerroneousbit.Wemay,therefore,haveHammingcodes 15,11 or 31,26 andsoon.
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Nowlet’sgobacktothepreviousexampleofQPSKworkingat 10 .Butthistimeusea 31,26 Hammingcode.Theuncoded 3.9 10 asbefore.Now,however,thechannelsymbolenergyovernoisedensityis 10 8.39. Thebiterrorratebeforeerror
correctionwillbe 2 8.39 4.1 2.066 10 .
1 0 1
or,1 1 31 1
wherep 2.066 10 and,therefore, 1.9 10 and 9.510 .Thisismorethananorderofmagnitudebetterthantheuncodedcase.
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DiscussingthesimpleexampleofusingHammingcodeorevenonlyasingleparitybit,hopefully,hasclarifiedforyoutheconceptofusingredundancyforthepurposeoferrordetectionanderrorcorrection.Itisclearthatdetectingtheexistenceoferrorsisbothsimpler intermsofdecodercomplexity andlesscostly requiringlessnumberofparitybitsand,therefore,requiringlessbandwidth .CyclicRedundancyCodes CRC areusedinordertodetecterrors.Afterdetectingerrors,thereceiverhastwooptions:1 todiscardtheerroneousdataand2 askthetransmittertoretransmitthecorrupteddataagain.ThelatteriscalledAutomaticRepeatRequest ARQ .ARQhastheadvantagedofbeingadaptivetochannelcondition.Whenthechannelisgood,therearenotmanyerroneouspacketsandtherefore,notmuchretransmission.So,theoverheadismostlythefewparitybitsusedfordetectingtheerrors.TheproblemwithARQis,however,thefactthatitisnotsuitablefordelaysensitivereal‐timetrafficsuchasvoiceandreal‐timevideo.Thisisparticularlytrueforlinkswithhightransmissiondelay.Takeasatellitelinkwheretheendtoenddelayiscloseto500milliseconds.Suchdelayisnottolerableinthecaseofvoiceandreal‐timevideo.Forreal‐timetraffic,enoughredundancyisaddedsothattheerrorscanbe
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Department of Electrical & Computer Engineering
SchemesallowingenoughredundancysothatthereceivercancorrecttheerroneouslyreceivedpacketsarecalledForwardErrorCorrection FEC schemes.UnlikeARQwheretheschemeadaptsitselftothechannelcondition,forFECthesystemshouldbedesignedwithanasaccurateaspossibleassessmentofthechannel.Ifthecodechosencorrectlessthanthenumberoferrorscreatedbythechannel,theerrorsremainuncorrectedandevenextraerrorsmaybeadded.Ontheotherhandifthecodeusediscapableofcorrectingmoreerrorsthanwhatthechannelcauses,theextraerrorcorrectingcapabilityiswasted,i.e.,wehavewastedbandwidthwithoutgaininganything.BlockCodesandConvolutionalCodes:Theerrorcorrectingcodesarebroadlydividedintotwocategories:blockcodesandconvolutionalcodes.Forablockcode,blocksof informationbitsentertheencoderandtheencoderoutputs bits.Inasystematicencoder,these bitsincludethe informationbitsplus paritybits.Ablockcodeencoder,afterencodingablockof bitsstartsworkingonthenext bitsandforgetsallaboutthepreviousblock,i.e.,ablockdoesnothaveanymemorybeyondtheblockonwhichitisworkingatagiventime.
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Department of Electrical & Computer Engineering
Theoutputofaconvolutionalencoder,ontheotherhand,doesnotonlydependonthecurrentinput,butalsoonthepreviousinputsand/oroutputs.
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Theabovefigureshowssimpleconvolutionalcodefortwobitsofmemory,hencefourstates.ThetwooutputsareformedbyXORing theinputandsomeofthepastinputs.Thisisarate½code.Theoperationofaconvolutionalencodercanbedescribedbyastatediagram,atreeoratrellis.Usingtrellisismorecommon.Followingistrellisrepresentationofarate½encoderwithmemorytwo:
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Thedecoderofaconvolutionalcodeconsistsofnaymechanismthatcangothroughthetrellisandfindstheonepaththatisclosesttothereceivedsequence.ThemostcommondecodingtechniqueistheViterbidecoder.Viterbidecodercaneitherbeusedafterdemodulation,.Insuchacaseitlooksforthepaththatdiffersinleastnumberofbitswiththeoutputofthedemodulator.ThenumberofplacesinwhichtwobinarysequencesaredifferentiscalledtheHammingdistance.So,inthiscase,thedecodertriestofindthepathwhoselabelshavetheminimumHammingdistancewiththedemodulatedsequence.ThisiscalledhardViterbidecoding.ItisalsopossiblethatthedecoderfindstheEuclideandistancebetweentheoutputofthereceiverfilterandthesequenceoflabelsofthepathsandfindsthepathwhosebranchlabelshavetheminimumHammingdistancefromthereceivedvalues.ThisiscalledsoftdecisionViterbidecoding.Softdecisiondecodinghasusuallyabout3dBadvantageoverdecision.TheconvolutionalcodeusedinDVBandmanyindustrialapplicationsisarate½64stateencoder,i.e.,onewith6memorylength 6Flip‐flopssavingthepastinputs .
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Theencoderforthiscodeis,
Onecanhaveotherratesbypuncturingtheoutputoftherate½encoder.Forexample,onecanfeedtwobitsattheinputandgetatotalof4outputs 2ateachoutputpoint .Deletingoneof4outputsonewillhavearate2/3code 2bitsin,3bitsout .
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Thistableshowsthepuncturingpatternforotherrates:
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FollowingisacomparisonoftheperformanceoftheconvolutionalcodewithsoftandhardViterbidecodingwiththeuncoded case:
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Thememoryoftheconvolutionalcodescausestheerrorstooccurinburst.Toseethisassumethatabitisdecodedinerror,i.e.,awrongpathhasbeenchosenonatrellis.Ittakesthedeocdeer atleastKstagestogetbackback totherighttrackwhereKistheconstraintlengthofthecodewhichisthenumberofmemorybitsplusone tocountforthepresentbitaswellasK‐1pastinputbits .
ThismeansthattheconvolutionalencodingturnsamemorylessAWGNchannelintoabursterrorchannel.InordertocombatthisReedSolomoncodesareusedinaconcatenationarrangement.TheinformationisfirstencodedusinganRSencoder calledtheoutercode andthentheoutputoftheRSencoderisencodedusingaconvolutionalencoder theinnercode .AtthereceiverfirsttheViterbidecoderisappliedtorecovertheinputoftheconvolutionalencoderandthenthe
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RSdecodingisperformed.ReedSolomon RS codesarenon‐binarycodes.Foreachinteger onecandefineanRScodewith 2 1symbols,eachsymbolconsistingof bits. ofthesymbolscanbetheinformationand symbolswillbetheparitysymbols.An , RScodecancorrectupto errors,where representsthefloorofx,i.e.,thelargestintegersmallerthanx.Example:Take 4.Then 2 1 15.Soeachcodewordconsistsof15symbolseachbeing4bitslong.Soeachcodeword willbe60bitslong.Taking,forexamplek 11,wewillhavea 15,11 RScodethatencodes11symbols4x11 44bits into15symbols 60bits .Itcancorrectupto2erroneous4bitsymbols.Example: TheRScodewithm 8isofparticularinterestaseachofthesymbolsrepresentabyte.Form 8,thecodelengthn 255.Thatiseachcodeword consistsof2558‐bitsymbols.Takingk 239,wewillhave 255,239 code.Thiscodeencodes239bytes 1912bits into255bytes 2040bits byappending16bytesofparity.Itcancorrectupto8erroneousbytes.So,itcancorrectanyerrorburstoflength7x8 56bits.
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Department of Electrical & Computer Engineering
AswediscussedearlierMPEG‐TSconsistsofpacketsoflength188bytes.IfwewantedtouseanRScodeoflength255,weneededtoadd67bytesofparitywhichistoomuchandresultsinunnecessarywastageofbandwidth.Inordertoavoidthis,wecanshortentheRScode.Wecanappendthe188databyteswith51bytesofzero 408zeros .SincetheRScodeissystematic,i.e.,thedataandparitypartsareseparateanddistinguishable,wecanomitthesezerospriortotransmissioninfactthesezerosarejustconceptual .Theresultwillbea 204,188 shortenedRScode.PerformanceEvaluationoftheRSCodes:WewilltrytofindanapproximatevaluefortheprobabilityoferrorusingReedSolomoncodes.Asitwasstatedabove,an n,k RScodecancorrectupto
erroneousm‐bitsymbols.IFthenumberoferrorsismorethan ,thensomeoralloftheerrorsremainun‐corrected.Itisevenpossiblethatthedecoderaddextraerrorsbytryingtocorrectsymbolsthatarenotinerror.Wetaketheworstcaseandassumethatifthereare errors,thedecodernotonlydoesnotcorrectanyofthe errors,butalsoadd errors.So,theprobabilityoferrorgiventhatwethereare errorsis .Theprobabilitythatareceivedcodeword
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Department of Electrical & Computer Engineering
has errorsis 1 where istheprobabilitythatasymbolisinerror.Lettheprobabilityofencodedbitsbeforedecodingbe .Then,
1 1Thebiterrorrate isdeterminedbasedonthemodulationschemeusedforexample,forQPSKitisgivenby,
2 2
Thereare sequencewith errorsamongthepossiblensymbolsequenceswhere,
!! !
.So,thesymbolerrorratewill,approximately,be:
1
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Assumingthatwhenasymbolerroroccurs,ontheaverage,halfthebitsareinerror,weget,
12
12 1
DVBExample:InDVBstandarda 204,188 RScodeisused,so,t 8.Thatis,thedecodercanrecoverallthe204bytelongTSpacketthathavelessthan9erroneousbytes.So,
12 204 8 204 1
AssumethatweareusingBPSKmodulationat 8 .
Theun‐codedBERis, , 2 10 . 3.55 1.92 10 .Nowlet’sseethatRScodecandoforus.TheBERofthecodedstreamafterthedemodulatorandbeforedecodingis,
2 2188204 10 . 3.25 10
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Thesymbolerrorratebeforedecodingis1 1 8 0.0026.
So,1
2 204 8 204 0.0026 1 0.0026
Sincethetermsaredecreasingrapidly,wecanusethefirsttermasalowerboundontheprobabilityoferror.Ifyoucalculatethetermfor 10 youseethatitisabout0.05ofthetermfor 9. So,
172 204
2049 0.0026 1 0.0026 4.6 10
