[paper][Communication] 1948 Shannon - A Mathematical Theory Of Communication

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1、AMathematicalTheoryofCommunicationByC.E.SHANNONINTRODUCTIONTHErecentdevelopmentofvariousmethodsofmodulationsuchasPCMandPPMwhichexchangebandwidthforsignal-to-noiseratiohasin-tensifiedtheinterestinageneraltheoryofcommunication.AbasisforsuchatheoryiscontainedintheimportantpapersofNyquist

2、’andHartley*onthissubject.Inthepresentpaperwewillextendthetheorytoincludeanumberofnewfactors,inparticulartheeffectofnoiseinthechannel,andthesavingspossibleduetothestatisticalstructureoftheoriginalmessageandduetothenatureofthefinaldestinationoftheinformation.Thefundamentalproblemofcomm

3、unicationisthatofreproducingatonepointeitherexactlyorapproximatelyamessageselectedatanotherpoint.Frequentlythemessageshavemea&g;thatistheyrefertoorarecorrelatedaccordingtosomesystemwithcertainphysicalorconceptualentities.Thesesemanticaspectsofcommunicationareirrelevanttotheengineering

4、problem.Thesignificantaspectisthattheactualmessageisoneselectedfromasetofpossiblemessages.Thesystemmustbedesignedtooperateforeachpossibleselection,notjusttheonewhichwillactuallybechosensincethisisunknownatthetimeofdesign.Ifthenumberofmessagesinthesetisfinitethenthisnumberoranymonotoni

5、cfunctionofthisnumbercanberegardedasameasureofthein-formationproducedwhenonemessageischosenfromtheset,allchoicesbeingequallylikely.AswaspointedoutbyHartleythemostnaturalchoiceisthelogarithmicfunction.Althoughthisdefinitionmustbegen-eralizedconsiderablywhenweconsidertheinfluenceofthest

6、atisticsofthemessageandwhenwehaveacontinuousrangeofmessages,wewillinallcasesuseanessentiallylogarithmicmeasure.Thelogarithmicmeasureismoreconvenientforvariousreasons:1.Itispracticallymoreuseful.Parametersofengineeringimportance*Nyquist,H.,“CertainFactorsAffectingTelegraphSpeed,”BellSy

7、sletnTechnicalJwr-nol,April1924,p.324;“CertainTopicsinTelegraphTransmissionTheory,”A.I.E.E.Ttans.,v.47,April1928,p.617.1Hartley,R.V.L.,“TransmissionofInformation,”BellSystemTeclanidJournal,July1928,p.535.Vol.27,PP.379.423,623.656,July,October,1948ReissuedDecember.1957Copyright1948byAM

8、ERICA