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1、CommunicationinthePresenceofNoiseCLAUDEE.SHANNON,MEMBER,IREClassicPaperAmethodisdevelopedforrepresentinganycommunicationsystemgeometrically.Messagesandthecorrespondingsignalsarepointsintwoªfunctionspaces,ºandthemodulationprocessisamappingofonespaceintotheother.Usingthisre
2、presentation,anumberofresultsincommunicationtheoryarededucedconcern-ingexpansionandcompressionofbandwidthandthethresholdeffect.Formulasarefoundforthemaximumrateoftransmissionofbinarydigitsoverasystemwhenthesignalisperturbedbyvarioustypesofnoise.Someofthepropertiesofªideal
3、ºsystemswhichtransmitatthismaximumratearediscussed.TheequivalentFig.1.Generalcommunicationssystem.numberofbinarydigitspersecondforcertaininformationsourcesiscalculated.perturbations.Distortioncan,inprinciple,becorrectedbyapplyingtheinverseoperation,whileaperturbationdueto
4、I.INTRODUCTIONnoisecannotalwaysberemoved,sincethesignaldoesnotAgeneralcommunicationssystemisshownschemati-alwaysundergothesamechangeduringtransmission.callyinFig.1.Itconsistsessentiallyoffiveelements.4)TheReceiver:Thisoperatesonthereceivedsignal1)AnInformationSource:Thesou
5、rceselectsonemes-andattemptstoreproduce,fromit,theoriginalmessage.sagefromasetofpossiblemessagestobetransmittedtoOrdinarilyitwillperformapproximatelythemathematicalthereceivingterminal.Themessagemaybeofvariousinverseoftheoperationsofthetransmitter,althoughtheytypes;forexa
6、mple,asequenceoflettersornumbers,asmaydiffersomewhatwithbestdesigninordertocombatintelegraphyorteletype,oracontinuousfunctionoftimenoise.,asinradioortelephony.5)TheDestination:Thisisthepersonorthingforwhom2)TheTransmitter:Thisoperatesonthemessageinthemessageisintended.som
7、ewayandproducesasignalsuitablefortransmissionFollowingNyquist1andHartley,2itisconvenienttousetothereceivingpointoverthechannel.Intelephony,thisalogarithmicmeasureofinformation.Ifadevicehasoperationconsistsofmerelychangingsoundpressureintopossiblepositionsitcan,bydefinition
8、,storelogunitsofaproportionalelectricalcurrent.Intelegraphy,wehaveinformation.Thechoiceofthebase
