《通信与电子信息科技英语》课件unit 2

ChannelCapacityNewwordsandphrases

1．abstractionn.抽象；抽象观念2．encompassvt.包括，包含3．devisevt.设计,发明4．wherebyadv.凭那个；由此5．arbitrarilyadv.任意地6．theoremn.定理7．infrequentadj.很少发生的,罕见的8．overridevt.压倒,制服，凌驾9．therebyadv.由此,因此,从而10．gaussianadj.高斯的

Gauss高斯(1777～1855,德国数学家、天文学家)11．unityn.一，单一12．complementaryadj.补充的；互补的ChannelCapacity13．derivationn.推导,导出，公式推导14．formidableadj.困难的，棘手的,可怕的15．undertakevt.进行,从事16．presumedadj.假定的,推测的

presumablyadv.推测起来,大概,估计,可能17．likelihoodn.可能,可能性likelyadj.可能，可能的18．intervaln.间隔，时间间隔19．roundingn.舍入(成整数);四舍五入20．abruptadj.不连续的，突然的，急剧的，陡的21．reliablyadv.可靠地，安全地，确实地22．heuristicadj.启发式的,渐进的23．intuitiveadj.直觉的;直观的intuitivelyadv.直觉地,直观地24．contemplatevt.预期(料)ChannelCapacity25．viceversaadv.反之亦然（viceversa)26．quantizevt.量化27．receptionn.接收28．extremeadj.极端的，极度的,偏激的29．attenuatevt.衰减，使衰减30．distortvt.失真，使失真distortionn.失真,畸变31．equalizern.均衡器32．recoverableadj.可恢复的 1enterinto

参加，成为……一部分，涉及2dueto

由于;起因于;归功于3besomethingof

有一点4inprinciple

原则上,大致上onprinciple按照原则（或道德标准）ChannelCapacity5providedthat

假如,设若6probabilityoferror(errorprobability)

误码率，误差概率7becloseto

接近,靠近8bandlimitedgaussianchannel

限带高斯信道9physicalsystem

物理系统,实际系统10turnout

（常与to,that连用）结果，结果是……11lowerbound

下界,下限12upperlimit

上限13rootmeansquare

均方根，均方根值；均方根(的)rootmeansquareerror

均方根(有效值)误差14amountofinformation

（informationcontent;quantityofinformation;informationquantity）信息量15ideallowpassfilter

理想低通滤波器ChannelCapacity16risetime

上升时间17asamatterofconvenience

为方便起见18whiteGaussiannoise(whitegaussiannoise)高斯白噪声19ontheotherhand

另一方面20tradeoff

交替换位，折衷选择(tradeoffn.折衷，权衡)21signaltonoiseratio

信号噪声比，信噪比（SNR,S/N）22befreeto

随意,任意,不受拘束23makeupfor

补偿ChannelCapacity

TheimportanceoftheconceptofinformationrateisthatitentersintoatheoremduetoShannonwhichisfundamentaltothetheoryofcommunications.Thistheoremisconcernedwiththerateoftransmissionofinformationoveracommunicationchannel.Whilewehaveusedthetermcommunicationchannelonmanyoccasions，itiswelltoemphasizeatthispoint,thattheterm,whichissomethingofanabstraction,isintendedtoencompassallthefeaturesandcomponentpartsofthetransmissionsystemwhichintroducenoiseorlimitthebandwidth.Ⅰ.Shannon’sTheorem,ChannelCapacityShannon’stheoremsaysthatitispossible,inprinciple,todeviseameanswherebyacommunicationssystemwilltransmitinformationwithanarbitrarilysmallprobabilityoferrorprovidedthattheinformationrateRislessthanorequaltoarateCcalledthechannelcapacity.Toputthemattermoreformally,wehavethefollowing:

ChannelCapacityTheoremGivenasourceofMequallylikelymessages,withM》1,whichisgeneratinginformationatarateR.GivenachannelwithchannelcapacityC.Then,ifR≤Cthereexistsacodingtechniquesuchthattheoutputofthesourcemaybetransmittedoverthechannelwithaprobabilityoferrorinthereceivedmessagewhichmaybemadearbitrarilysmall.TheimportantfeatureofthetheoremisthatitindicatesthatforR≤Ctransmissionmaybeaccomplishedwithouterrorinthepresenceofnoise.Thisresultissurprising.Forinourconsiderationofnoise,say,gaussiannoise,wehaveseenthattheprobabilitydensityofthenoiseextendstoinfinity.Weshouldthenimaginethattherewillbesometimes,howeverinfrequent,whenthenoisemustoverridethesignaltherebyresultinginerrors.However,Shannon’stheoremsaysthatthisneednotcauseamessagetobeinerror.

ChannelCapacityThereisanegativestatementassociatedwithShannon’stheorem.Itstatesthefollowing:TheoremGivenasourceofMequallylikelymessages,withM》1,whichisgeneratinginformationatarateR;thenifR＞Ctheprobability

theprobabilityoferrorisclosetounityforeverypossiblesetofMtransmittersignals.ThisnegativetheoremstatesthatiftheinformationrateRexceedsaspecifiedvalueC,theerrorprobabilitywillincreasetowardunityasMincreases,andthatalso,generally,inthiscasewhereR＞C,increasingthecomplexityofthecodingresultsinanincreaseintheprobabilityoferror.Ⅱ.CapacityofaGaussianChannelAtheoremwhichiscomplementarytoShannon’stheoremandappliestoachannelinwhichthenoiseisgaussianisknownastheShannonHartleytheorem.

ChannelCapacityTheoremThechannelcapacityofawhite,bandlimitedgaussianchannelisC=Blog2(1+S/N)bits/s(2.1)whereBisthechannelbandwidth,Sisthesignalpower,andNisthetotalnoisewithinthechannelbandwidth,thatis,N=B,with1/2the(two-ided)powerspectraldensity.Thistheorem,althoughrestrictedtothegaussianchannel,isoffundamentalimportance.First,wefindthatchannelsencounteredinphysicalsystemsgenerallyare,atleastapproximately,gaussian.Second,itturnsoutthattheresultsobtainedforagaussianchanneloftenprovidealowerboundontheperformanceofasystemoperatingoveranongaussianchannel.Thus,ifaparticularencoderdecoderisusedwithagaussianchannelandanerrorprobabilityPeresults,thenwithanongaussianchannelanotherencoderdecodercanbedesignedsothatthePewillbesmaller.WemaynotethatchannelcapacityequationscorrespondingtoEq.(2.1)havebeenderivedoranumberofnongaussianchannels.

ChannelCapacityThederivationofEq.(2.l)forthecapacityofagaussianchannelisratherformidableandwillnotbeundertaken.However,theresultmaybemadetoappearreasonablebythefollowingconsiderations.

Supposethat,forthepurposeoftransmissionoverthechannel,themessagesarerepresentedbyfixedvoltagelevels.Then,asthesourcegeneratesonemessageafteranotherinsequence,thetransmittedsignals(t)takesonawaveformsimilartothatshowninFig.2.1.

Ⅰ.PleasetranslatethefollowingwordsandphrasesintoCbabilitydensity7.rootmeansquare8.tradeoff9.lowerbound1.equalizer11.viceversa12.upperlimit

Exercises物理系统，实际系统上升时间信息量理论上，原则上高斯信道概率密度均方根值,均方根；均方根(的)交替换位，折衷选择下界,下限均衡器反之亦然上限Ⅱ.PleasetranslatethefollowingwordsandphrasesintoEnglish.1.通信理论2.香农定理3.信道带宽4.信号波形5.理想低通滤波器6.自相关函数7.无噪声高斯信道8.通信信道9.信息速率10.信噪比Exercisescommunicationtheory(theoryofcommunications)Shannon’stheoremchannelbandwidthsignalwaveformideallowpassfilterautocorrelationfunctionnoiselessgaussianchannelcommunicationchannelinformationrateSignaltonoiseratio（SNR,S/N）Exercises11.信道容量12.双边功率谱密度13.误码率14.奈奎斯特采样速率15.限带高斯信道16.高斯白噪声channelcapacityTwosidedpowerspectraldensityerrorprobability(probabilityoferror)NyquistsamplingratebandlimitedgaussianchannelwhiteGaussiannoiseExercisesⅢ.Fillintheblankswiththemissingword(s).

1.Thereisanegativestatementassociated

Shannon’stheorem.2.

thepurposeoftransmissionoverthechannel,themessagesarerepresentedbyfixedvoltagelevels.3.SincethetransmissionofanyoftheMmessagesisequallylikely,H=log2M,thusourchannelistransferringinformation

arateR=rH.4.Forafixedsignalpowerand

thepresenceofwhitegaussiannoisethechannelcapacityapproachesanupperlimitwithincreasingbandwidth.5.Itis

greatinteresttorecognizethatthetradeoffbetweenbandwidthandsignaltonoiseratioisnotlimitedbyalowerlimit

bandwidth.withonatinofinExercises6.Thesignalistransmitted

achannelwhichcanberepresentedasalowpassRCcircuitwithcutoffat1Hz.7.Ifthereisnonoise,thenweareentirelyfreetomake

fortheattenuationbytheuseofanamplifierandtocorrectthefrequencydistortionbytheuseofanequalizer.8.Thatis,weneedtoestimatetheintervalTwhichshouldbeassignedtoeachmessagetoallowthetransmittedlevelstoberecognizedIndividually

thereceiver,eventhoughthebandwidthBofthechannelislimited.9.Therefore,the25percentreduction

bandwidthrequiresa60percentincrease

signalpower.inasinofoverExercises10.Whilewehaveusedthetermcommunicationchannel

manyoccasions,itiswelltoemphasizeatthispoint,thattheterm,whichisSomething

anabstraction,isintendedtoencompassallthefeaturesandcomponentpartsofthetransmissionsystemwhichintroducenoiseorlimitthebandwidth.11.Theprobabilityoferrorisclose

unityforeverypossiblesetofMtransmittersignals.12.Itturnsout

theresultsobtainedforagaussianchanneloftenprovidealowerbound

theperformanceofasystemOperating

hatintoinasⅣ.Answerthefollowingquestionsaccordingtothetext.1.WhatisShannonHartleytheorem?2.PleasedescribeShannon’stheoreminyourownwordsinEnglish.

ExercisesShannonHartleytheorem:Thechannelcapacityofawhite,bandlimitedgaussianchannelisC=Blog2(1+S/N)bits/s,whereBisthechannelbandwidth,Sisthesignalpower,andNisthetotalnoisewithinthechannelbandwidth,thatis,N=ηB,withη/2the(twosided)powerspectraldensity.GivenasourceofMequallylikelymessages,withM1,whichisgeneratinginformationatarateR.GivenachannelwithchannelcapacityC.Then,ifR≤C,Thereexistsacodingtechniquesuchthattheoutputofthesourcemaybetransmittedoverthechannelwithaprobabilityoferrorinthereceivedmessagewhichmaybemadearbitrarilysmall.3.TrytodescribeShannon’stheorembyanegativestatementinEnglish.4.WhyistheShannonHartleytheoremimportant?