《通信與電子信息科技英語(yǔ)》課件unit 2

ChannelCapacityNewwordsandphrases

1．a(chǎn)bstractionn.抽象；抽象觀念2．encompassvt.包括，包含3．devisevt.設(shè)計(jì),發(fā)明4．wherebyadv.憑那個(gè)；由此5．a(chǎn)rbitrarilyadv.任意地6．theoremn.定理7．infrequentadj.很少發(fā)生的,罕見(jiàn)的8．overridevt.壓倒,制服，凌駕9．therebyadv.由此,因此,從而10．gaussianadj.高斯的

Gauss高斯(1777～1855,德國(guó)數(shù)學(xué)家、天文學(xué)家)11．unityn.一，單一12．complementaryadj.補(bǔ)充的；互補(bǔ)的ChannelCapacity13．derivationn.推導(dǎo),導(dǎo)出，公式推導(dǎo)14．formidableadj.困難的，棘手的,可怕的15．undertakevt.進(jìn)行,從事16．presumedadj.假定的,推測(cè)的

presumablyadv.推測(cè)起來(lái),大概,估計(jì),可能17．likelihoodn.可能,可能性likelyadj.可能，可能的18．intervaln.間隔，時(shí)間間隔19．roundingn.舍入(成整數(shù));四舍五入20．a(chǎn)bruptadj.不連續(xù)的，突然的，急劇的，陡的21．reliablyadv.可靠地，安全地，確實(shí)地22．heuristicadj.啟發(fā)式的,漸進(jìn)的23．intuitiveadj.直覺(jué)的;直觀的intuitivelyadv.直覺(jué)地,直觀地24．contemplatevt.預(yù)期(料)ChannelCapacity25．viceversaadv.反之亦然（viceversa)26．quantizevt.量化27．receptionn.接收28．extremeadj.極端的，極度的,偏激的29．a(chǎn)ttenuatevt.衰減，使衰減30．distortvt.失真，使失真distortionn.失真,畸變31．equalizern.均衡器32．recoverableadj.可恢復(fù)的 1enterinto

參加，成為……一部分，涉及2dueto

由于;起因于;歸功于3besomethingof

有一點(diǎn)4inprinciple

原則上,大致上onprinciple按照原則（或道德標(biāo)準(zhǔn)）ChannelCapacity5providedthat

假如,設(shè)若6probabilityoferror(errorprobability)

誤碼率，誤差概率7becloseto

接近,靠近8bandlimitedgaussianchannel

限帶高斯信道9physicalsystem

物理系統(tǒng),實(shí)際系統(tǒng)10turnout

（常與to,that連用）結(jié)果，結(jié)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)誤差14amountofinformation

（informationcontent;quantityofinformation;informationquantity）信息量15ideallowpassfilter

理想低通濾波器ChannelCapacity16risetime

上升時(shí)間17asamatterofconvenience

為方便起見(jiàn)18whiteGaussiannoise(whitegaussiannoise)高斯白噪聲19ontheotherhand

另一方面20tradeoff

交替換位，折衷選擇(tradeoffn.折衷，權(quán)衡)21signaltonoiseratio

信號(hào)噪聲比，信噪比（SNR,S/N）22befreeto

隨意,任意,不受拘束23makeupfor

補(bǔ)償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物理系統(tǒng)，實(shí)際系統(tǒng)上升時(shí)間信息量理論上，原則上高斯信道概率密度均方根值,均方根；均方根(的)交替換位，折衷選擇下界,下限均衡器反之亦然上限Ⅱ.PleasetranslatethefollowingwordsandphrasesintoEnglish.1.通信理論2.香農(nóng)定理3.信道帶寬4.信號(hào)波形5.理想低通濾波器6.自相關(guān)函數(shù)7.無(wú)噪聲高斯信道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.雙邊功率譜密度13.誤碼率14.奈奎斯特采樣速率15.限帶高斯信道16.高斯白噪聲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?