1ErrorControlCodingErrorControlStrategies,PerformanceMeasuresOutlineErrorControlStrategiesForwardErrorCorrection(FEC)AutomaticRepeatRequest(ARQ)HybridARQPerformanceMeasures

Probabilityofdecodingerror(errorprobability)CodinggainShannonLimit2ForwardErrorCorrection(FEC)One-waysystem,evennotstrictlyone-wayDigitalstoragesystems,deep-spacecommunicationsystemsandmostofthecodedsystemsinusetodayAutomaticRepeatRequest(ARQ)Two-waysystemsomedatanetworksandsatellitecommunicationsystemsErrorControlStrategies3FECEmployerror-correctingcodesAutomaticallycorrecterrorsdetectedatreceiverThisbookisdevotedmostlytotheanalysisanddesignofFECsystem4ARQStop-and-waitARQContinuousARQGobackNSelectivereject(selectiveretransmission)5Stop-and-waitARQVSContinuousARQContinuousARQismoreefficientContinuousARQismoreexpensiveStop-and-waitARQdesignedforhalf-duplexchannelsContinuousARQdesignedforfull-duplexchannels6ARQVSFECARQrequiresmuchsimplerdecodingequipment(Actuallyonlydetectingnocorrecting)ARQisadaptiveinthesensethatinformationisretransmittedonlywhenerrorsoccurWhenerrorrateishigh,thesystemthroughputisloweredbyusingARQAhybridcombinationofFECismoreefficientthanARQalone7Howtomeasuretheperformanceofacodedsystem?(AcurveofBERvs)Probabilityofdecodingerror(errorprobability)---YdirectionCodinggain---XdirectionPerformanceMeasures8Errorprobability(WERandBER)Probabilityofword(orblock)error---WER---WorderrorrateProbabilityofbiterror---BER---BiterrorrateThesetwoerrorprobabilitiesshouldbekeptaslowaspossibleErrorProbability9ErrorProbability(RelationbetweenEbandEs)Theenergy-per-informationbit:energypertransmittedsymbolR:coderate,R=k/ncommonlyusedtoexpresserrorprobability:one-sidedPSD(PowerSpectrumDensity)ofthechannelnoise10ErrorProbability---Ydirection11

3.7dBCodinggainThereductionintheEb/Norequiredtoachieveaspecificerrorprobability(BERorWER)CodinggainisimportantincommunicationapplicationsCodingthresholdistheSNRatwhichthecodinggainactuallybecomesnegativeAsymptoticcodinggain——thecodinggainforlargeSNR12Codinggain13CodingthresholdCodinggain14ShannonLimitDefinition:theminimumSNRrequired----error-free----codedsystem----coderateRMeaning:SNRshouldexceedsShannonlimitUse:measurethemaximumachievablecodinggain15----error-free----AWGN----BPSK----codedsystem----R=0.5

----Shannonlimit:0.188dBFigureofShannonlimit0.188dBR=0.516R:0~0.99Eb/No:ShannonlimitExample:----AWGNchannel----BPSK

----10^-5--uncodedsystem:9.65dB

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codedR=0.5:0.188dB--(codinggain)max:9.462dB(Soyoucancomparedifferentcodingschemestoseewhichoneisbetter)TableofShannonlimit(Ref.ShuLin)BERPerformanceofConvolutionalCode17Codinggain:

4.15dB(Codinggain)max:

9.462dBImprovementgap:3.962dBShannonlimit: