雨课堂学堂在线学堂云《信息论与编码（中山）》单元测试考核答案

第1题Whichofthefollowingphysicalquantitiesdoesnotsatisfynon-negativity?AH(X)BI(X;Y)CH(X|Y)DI(xj;yj)第2题If𝑋isuniformlydistributedoverx1,x2,...,xU,i.e.,

P1=P2=...=PU=1U,thenH(x)=_____.Alog2UB2log2UClog2(U+1)DUlog2U第3题Thenaturalnessofthedefinitionofjointentropyandconditionalentropyisexhibitedbythefactthattheentropyofapairofrandomvariablesistheentropyofoneplustheconditionalentropyoftheother.第4题SupposethatthesourceXcontainsfourdifferentdiscretemessages.IfandonlyiftheprobabilityofeachmessageinXis____,thesourceentropyreachesthemaximumvalue.正确答案：:0.25第5题Assumethatwehaveahorseracewithtwohorsestakingpartandtheprobabilitiesofwinningforthetwohorsesare(0.5,0.5).Wecancalculatetheentropyofthehorseraceas

____bits.正确答案：:1第6题If𝑋and𝑌areindependent,then𝐼(𝑋,𝑌)=____.正确答案：:0第7题Informationcanbeincreasedbydataprocessing.第8题Therelativeentropyisameasureofthedistancebetweentwodistributions.第9题MutualinformationI(X,Y)describestheamountofinformationonevariableXcontainsabouttheotherY.第10题Bothinevitableandimpossibleeventshavezeroself-information.第11题If𝑋and𝑌areindependent,𝐻(𝑋|Y)=𝐻(Y)第12题Whichofthefollowingstatementsarecorrect?AIf𝑋and𝑌areindependent,I(𝑋;Y)=𝐻(X).BIf𝑋and𝑌areindependent,𝐻(𝑋|Y)=𝐻(X)CDeterministicsignaldoesnothaveinformationamount.DMutualinformationI(X;Y)representsthereductioninuncertaintyaboutXafterreceivingY.正确答案：BCD第13题IfI(X;Y)=0,whichofthefollowingoptionsarewrong?AH(X|Y)=H(Y|X)BH(X)=H(Y)CH(X,Y)<H(X)+H(Y)DH(X,Y)=H(X)+H(Y)正确答案：ABC第14题Assumethatthereare68studentsinourclass,andwewouldliketousebitstodistinguisheachofthem.Howmanybitsdoweneed?A6B4C7D2第15题Whichofthefollowingsentencescontainsthemostinformation?AIwillbeoneyearoldernextyear.BIwasbornin1993.CIwasbornin1990s.DIwasbornonNov.21,1993.第1题GivenadiscretechannelwithtransitionprobabilityofP(y=0|x=0)=0.5,P(y=1|x=0)=0.5,P(y=2|x=0)=0,P(y=0|x=1)=0,P(y=1|x=1)=0.5andP(y=2|x=1)=0.5.Thechannelcapacityis____.(bits/symbol)(inputnumberwiththedecimalpointonly)

正确答案：:0.5第2题GivenadiscretememorylesschannelY=(X+Z)mod11,whereZisgivenbyP(Z=1)=1/3,P(Z=2)=1/3,P(Z=3)=1/3,andXin{0,1,2,…,10}.AssumingthatZisindependentofX,whatisthecapacityofthischannel?

(logwithbase2inanswers)Alog(11)

(bits/symbol)Blog(8)

(bits/symbol)Clog(11)-log(3)

(bits/symbol)Dlog(8)-log(3)

(bits/symbol)第3题GivenadiscretebinarychannelwithtransitionprobabilityofP(y=0|x=0)=1,P(y=1|x=0)=0,P(y=0|x=1)=0.5,P(y=1|x=1)=0.5.Theprobabilityofx=0thatreachthechannelcapacityis

____.

(inputnumberwiththedecimalpointonly)正确答案：:0.6第4题GivenadiscretebinarychannelwithtransitionprobabilityofP(y=0|x=0)=0.4,P(y=1|x=0)=0.6,P(y=0|x=1)=0.4,P(y=1|x=1)=0.6.Thechannelcapacityis

____(bits/symbol).(inputnumberwiththedecimalpointonly)正确答案：:0第5题GivenanAWGNchannelwithSNR=Eb*R/(N0*W),whereWisbandwidth.IfSNRis4dBandWis2MHz,theoretically,wecantransmit30MegaBytesofdatain1minute.第6题Shannon'sChannelCodingTheoremstatesthatusingbinarymodulation,reliablecommunicationispossibleifr<C,whereristhecodingrateandCischannelcapacity.第7题WhicharetheequivalentexpressionsofI(X;Y)?AH(X)-H(Y|X)BH(Y)-H(Y|X)CH(X,Y)-H(X)-H(Y)DH(X)+H(Y)-H(X,Y)正确答案：BD第8题GivenanAWGNchannelwithy=x+n,and

xhasbinaryinput{-t,t}andn∼N(0,r2)

.Usingharddecisiondecoding(ify<0set

y=-t;

elsesety=t)atreceivingside,whatistheerrorprobability?(Q(x)isdefinedasthetailprobability,thatisPr(X>x),overastandardGaussiandistributionN(0,1))AQ(tr)BQ(t2r)CQ(2tr)DQ(t22r2)第9题GivenaBSCchannelwitherrorprobabilitycomputedabove,andacorrespondingAWGNchannelwhichhasthesameSNRt2r2.AtSNRof0.2dB,whichoneisclosesttothegapofchannelcapacitybetweenthetwochannels?(bits/symbol)A0.5B0.3C0.15D0.05第10题Givenadiscreteternary(3inputand3output)symmetricchannelwitherrorprobabilityp.Atwhatvalueofpminimizethechannelcapacity?A0.5B0.25C0.333D0.167第11题InBSC,thelargertheerrorprobabilityp,thesmallerthechannelcapacity.第12题WhicharethecorrectexpressionsaboutI(X;Y)?AI(X;Y)<=H(X)BI(X;Y)>=H(X,Y)CI(X;Y)>=H(X|Y)DI(X;Y)<=H(X)+H(Y)正确答案：AD第13题GivenanAWGNchannelwithchannelmodey=x+n,whythechannelcapacityonlydefinestheunachievabletransmissionlimit?ABecausethechannelsignal-to-noiseratio(SNR)isnotlargeenoughBBecausewecannotperformmaximumlikelyhooddecodingatthereceiversideCBecauseinapracticalcommunicationsystem,xwillnotbenormaldistributedDBecausewecannotmeasurechannelnoiseprecisely第14题Givenadiscreten-arysymmetricchannelwitherrorprobabilityp,whatisthechannelcapacity?(logwithbase2inanswers)A1+p·log(p)+(1-p)·log(p)(bits/symbol)Blog(n)+(1-np)·log(1-np)+(n-1)p·log(p)(bits/symbol)Clog(n)+(n-1)(1-np)·log(1-np)+p·log(p)(bits/symbol)Dlog(n)+(n-1)(1-p)·log(1-p)+p·log((n-1)p)(bits/symbol)第15题WhatismeaningofmutualinformationI(X;Y)?ATheamountofuncertaintyaboutXthathasbeenreducedbyY,andviceversa.BTheuncertaintyofXgivenY,andviceversa.Homework-3.SourceCoding第1题Foroptimalsourcecodes,whatistheupperboundoftheexpectedlength?AHD(x)+2BHD(x)−1CHD(x)DHD(x)+1第2题Foroptimalsourcecodes,whatisthelowerboundoftheexpectedlength?AHD(x)+2BHD(x)−1CHD(x)DHD(x)+1第3题Whatisthepurposeofsourcecoding?AImprovetheefficiencyofdatatransmission.BImprovethereliabilityofdatatransmission.CImprovethebandwidthofdatatransmission.DReducetheerrorrateofdatatransmission.第4题Sourcesymbolshaveunambiguousrepresentation.Thatisthe()ofsourcecoding.AinstantaneouscodeBuniquelydecodableCnon-singularityDodevity第5题Acodewordcanonlybeuniquelydecodedintoasourcesymbol.Thusthiscodeis().AinstantaneouscodeBuniquelydecodableCnon-singularityDodevity第6题Nocodewordisaprefixofanyothercodeword.Thusthiscodeisan().AinstantaneouscodeBuniquelydecodableCnon-singularityDodevity第7题Whichcodeisaninstantaneouscode?A{0,10,1100,1101,1110,1111}B{0,10,1100,1101,1110,1011}C{0,10,110,1110,1011,1101}D{0,10,110,1110,1011,1100}第8题IsthereanyinstantaneouscodesforthefollowingDandlengths?AD=2,Length:1,2,3,3,3BD=2,Length:1,2,2,3,4CD=3,Length:1,1,1,2,4DD=3,Length:1,1,2,2,4第9题WhatisanecessaryandsufficientconditionofKraftinequality?AuniquelydecodabilityBinstantaneousnessCnon-singularityDodevity第10题Whichcodesaretheinstantaneouscodes?A{0,10,1100,1101,1110,1111}B{0,10,1100,1001,1110,1011}C{0,10,110,1110,1011,1111}D{0,10,110,1110,1011,1100}正确答案：AC第11题IsthereanyinstantaneouscodesforthefollowingDandlengths?AD=2,length:1,2,3,5,6BD=2,length:1,2,3,4,4CD=3,length:1,1,1,2,4DD=3,length:1,1,1,2,3正确答案：AB第12题{0,10,1100,1101,1110,1111}is____.AauniquelydecodablecodeBaninstantaneouscodeCanonsingularcodeDanoptimalcode正确答案：ABC第13题Whatarethefeaturesofarithmeticcoding?AUniquelydecodabilityBInstantaneousnessCNon-singularityDVariable-length正确答案：ABCD第14题WhatarethefeaturesofHuffmancoding?AUniquelydecodabilityBInstantaneousnessCNon-singularityDOptimalcode正确答案：ABCD第15题Thepurposeofsourcecodingistoimprovethereliabilityofcommunicationandperformanti-interferencecodingorerrorcontrolcoding.Homework-4.ChannelCoding第1题A101110011100100111001B001110011100101111001C101110011100100101001D101110011000100111001第2题A0111011B0111001C0111101D0111000第3题第4题____正确答案：:3第5题Let

g(x)=x3+x+1bethegeneratorpolynomialofa(7,4)cycliccodeoverGF(2).ThegeneratormatrixofthecodeinsystematicformcanbedefinedasG=[

].A1000101010011100101100001011B1000101010011100101000001011C1000001010011100101100001011D1000101010011100100100001011第6题Givenacodewithcodedimensionofkandcodelengthofn(n≥k),thenthecoderateofthecodeis(

).Ak/nBn/kCn-kD(n-k)/n第7题Givenarepetitioncodewithcodedimensionofkandcodelengthofn(n≥k),andletddenotetheminimumHammingdistanceofthecode,thenwehave(

).Ak=1;d=n-kBk=1;d=n-k+1Ck=0;d=n-kDk=0;d=n-k+1第8题Givenageneratorpolynomial

g(x)=x3+x2+1andthemessagepolynomial

m(x)=x3+x,thenthecodewordpolynomialcanbederivedas

c(x)=

().Ax6+x5+x4+xBx6+x5+x4+1Cx6+x5+x3+xDx6+x5+x3+1第9题Linearblockcodesinclude().AHammingcodesBReed-SolomoncodesCLDPCcodesDConvolutionalcodes正确答案：ABC第10题Givenacodewordfromacycliccodeasc=(1,0,0,1,1,1,0,1),then()isalsoacodewordinthesamecodebook.A(0,1,1,1,0,1,0,1)B(1,1,1,0,1,1,0,0)C(1,0,1,1,0,0,1,1)D(0,1,0,0,1,1,1,0)正确答案：BC第11题Shannon'sChannelCodingTheoremdemonstrateserrorfreetransmissionispossiblebymanipulatingrateofthecodeaccordingtothechannelcapacity.第12题Basedontheencoderstructure,channelcodescanbecategorizedintoblockcodesandconvolutionalcodes.第13题Hammingcodesarelinearblockcodes.第14题Basedonthemajoritydecoder,the(n,1,n)repetitioncodecancorrectupton/2errors.第15题Acycliccodeisablockcode,whichhasthepropertythatcyclicallyshiftingacodewordresultsinanothercodeword.Homework-5.ConvolutionalCodesandTrellisCodedModulation第1题Whichoneistheencoderstructureof

(15,13)8convolutionalcodes?ABCD第2题Pleasecalculatetheoutputoftheconvolutional

codeundertheinputu=[101100].(note:outputsequenceinformof[c1(1)c2(1)......c1(6)c2(6)])A[11,10,00,01,01,11]B[11,11,00,01,01,11]C[11,11,00,01,10,01]D[10,10,00,01,01,11]第3题Pleaseusethetrellistodeterminethecodewordthatcorrespondstomessage[11010].(Note:initialstatementS0S1=00)A[11,01,01,11,10]B[11,01,10,00,10]C[11,01,01,00,10]D[01,01,01,00,10]第4题Giventheencoderstructureofthe(7,5)8

convolutionalcode

asfollows,pleasedeterminethegeneratorsequences

g(1)andg(2).Ag(1)=[001],g(2)=[001]Bg(1)=[111],g(2)=[101]Cg(1)=[001],g(2)=[101]Dg(1)=[111],g(2)=[111]第5题GiventhepathmetricsandthebranchmetricsintheViterbidecodingasfollows,pleasetracebackthecodewordtodeterminethedecodingoutput.ADecodingoutput:0010110BDecodingoutput:0110100CDecodingoutput:0010100DDecodingoutput:1011100第6题The

Euclideandistancebetweenthereceivedsymbol(0.4,0.8)andthemodulationsymbol(1,0)is

().A1.5B0.8C1D1.2第7题WhatcanbeusedasthedecodingmetricsoftheViterbidecoding?AHammingdistanceBEuclideandistanceCAposterioriprobabilityDAprioriprobability正确答案：ABC第8题WhichofthefollowingprobabilitieswillbedeterminedduringtheBCJRalgorithm?(utand

ytdenotethemessagesymbolandthereceivedsymbolattimet,respectively.

ct1and

ct2arethecodewordsymbols.)AP(ut=0|yt)BP(ut=1|yt)CP(ct1=0|yt)DP(ct2=1|yt)正确答案：ABCD第9题ThefreedistanceoftheconvolutionalcodefromthisViterbitrellisis____.正确答案：:5第10题Thespectralefficiencyoftherate1/2convolutionalcodedsystemusingBPSKmodulationis____.正确答案：:0.5第11题Themissingpathmetric(inredblock)ofthesoftViterbidecodingtrellisis____.正确答案：:6.46第12题Encoderoutputattimetdependsonlyontheinputandthememoryunitsstatusattimet.第13题Errorcorrectioncapabilityofaconvolutionalcodecanbeimprovedbyincreasingthenumberofencoderstates.第14题Theencoderstructureshowedasbelowisasystematiccode.第15题Convolutionalcodewithasmallnumberofstateswillhaveagreatfreedistance.Homework-6.TurboCodes第1题Turbocodewasinventedby____in1993.AC.BerrouetalBA.J.ViterbiCL.R.BahletalDC.E.Shannon第2题Aturbocodeintegratesacoupleof_____codesinaparallelencodingstructure,whichcalledtheconstituentcodesoftheturbocode.AHammingBconvolutionalCReed-SolomonDrepetition第3题The______decodersareimplementedintheturbodecoding.AHard-inputHard-outputBHard-inputSoft-outputCSoft-inputHard-outputDSoft-inputSoft-output第4题GivenaSISOdecoderwithaprioriprobabilityPaandaposterioriprobabilityPp,wecancalculatetheExtrinsicprobabilitybyPe=____.APa-PpBPa/PpCPp-PaDPp/Pa第5题AnerrorflooroftheturbocodesathighSNRaredueto____.AasmallfreedistanceBthepresenceoflowweightcodewordsCahighcoderateDalongcodelength正确答案：AB第6题Theturbocodescancontrolthecoderatebypuncturing.第7题Themotivationofhavinganinterleaverbetweenthetwoencodersistoavoidthelowweightconvolutionalcodewordsandsubsequentlythelowweightturbocodewordbeingproduced.第8题Thenumberofiterationsisanimportantparameteraffectingthedecodingperformanceofturbocodes.第9题ThebetterdecodingperformanceofTurbocodescanbeachievedwiththemoreiterations.第10题Turbodecodingisnotlimitedtodecodeturbocodes,buttoanyconcatenated(serialorparallel)code.第11题Givenaturbocodewhoseconstituentcodeisthe

(1,5/7)8convolutionalcodeandtheturbocode'sencodingstructureasbelow,theinterleavingpatternisΠ=(2,5,1,3,4).Givenaninputmessageofu=(00001).Withoutpuncturing,theturbocodewordisc=___.A(000010010010111)B(000010010111010)C(000010