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1、EEEEntropyandInformationTheoryRobertM.GrayEntropyandInformationTheorySecondEditionRobertM.GrayDepartmentofElectricalEngineeringStanfordUniversityStanford,CA94305-9510USArmgray@stanford.eduISBN978-1-4419-7969-8e-ISBN978-1-4419-7970-4DOI10.1007/978-1-4419-7970-4SpringerNewYorkDordrechtHeid
2、elbergLondonLibraryofCongressControlNumber:2011920808©SpringerScience+BusinessMedia,LLC2011Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexc
3、erptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimila
4、rterms,eveniftheyarenotidentiÞedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)toTim,Lori,Julia,Peter,Gus,Amy,andAliceandinmemoryofTinoPrefaceThisbookisdev
5、otedtothetheoryofprobabilisticinformationmeasuresandtheirapplicationtocodingtheoremsforinformationsourcesandnoisychannels,withastrongemphasisonsourcecodingandstationarycodes.TheeventualgoalisageneraldevelopmentofShannon’smathe-maticaltheoryofcommunicationforsingleusersystems,butmuchofthe
6、spaceisdevotedtothetoolsandmethodsrequiredtoprovetheShannoncodingtheorems,especiallythenotionsofsources,channels,codes,entropy,information,andtheentropyergodictheorem.Thesetoolsformanareacommontoergodictheoryandinformationtheoryandcompriseseveralquantitativenotionsoftheinformationinran-d
7、omvariables,randomprocesses,anddynamicalsystems.Examplesareentropy,mutualinformation,conditionalentropy,conditionalinforma-tion,andrelativeentropy(discrimination,Kullback-Leiblerinformation,informationaldivergence),alongwiththelimitingnormalizedversionsofthesequantitiessu
