【Shannon，1948】A Mathematical Theory of Communication .pdf

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1、FromTheMathematicalTheoryofCommunication,c1949bytheBoardofTrusteesoftheUniversityofIllinois.UsedwiththepermissionofUniversityofIllinoisPress.AMathematicalTheoryofCommunicationByC.E.SHANNONINTRODUCTIONHErecentdevelopmentofvariousmethodsofmodulationsuchasPCMandPPMw

2、hichexchangebandwidthforsignal-to-noiseratiohasintensifiedtheinterestinageneraltheoryofcommunication.ATbasisforsuchatheoryiscontainedintheimportantpapersofNyquist1andHartley2onthissubject.Inthepresentpaperwewillextendthetheorytoincludeanumberofnewfactors,inparticu

3、lartheeffectofnoiseinthechannel,andthesavingspossibleduetothestatisticalstructureoftheoriginalmessageandduetothenatureofthefinaldestinationoftheinformation.Thefundamentalproblemofcommunicationisthatofreproducingatonepointeitherexactlyorap-proximatelyamessageselect

4、edatanotherpoint.Frequentlythemessageshavemeaning;thatistheyrefertoorarecorrelatedaccordingtosomesystemwithcertainphysicalorconceptualentities.Thesesemanticaspectsofcommunicationareirrelevanttotheengineeringproblem.Thesignificantaspectisthattheactualmessageisonese

5、lectedfromasetofpossiblemessages.Thesystemmustbedesignedtooperateforeachpossibleselection,notjusttheonewhichwillactuallybechosensincethisisunknownatthetimeofdesign.Ifthenumberofmessagesinthesetisfinitethenthisnumberoranymonotonicfunctionofthisnumbercanberegardedas

6、ameasureoftheinformationproducedwhenonemessageischosenfromtheset,allchoicesbeingequallylikely.AswaspointedoutbyHartleythemostnaturalchoiceisthelogarithmicfunction.Althoughthisdefinitionmustbegeneralizedconsiderablywhenweconsidertheinfluenceofthestatisticsofthemessa

7、geandwhenwehaveacontinuousrangeofmessages,wewillinallcasesuseanessentiallylogarithmicmeasure.Thelogarithmicmeasureismoreconvenientforvariousreasons:1.Itispracticallymoreuseful.Parametersofengineeringimportancesuchastime,bandwidth,numberofrelays,etc.,tendtovarylin

8、earlywiththelogarithmofthenumberofpossibilities.Forexample,addingonerelaytoagroupdoublesthenumberofpossiblestatesoftherelays.Itadds1tothebase2logarithmofthisnu