entropy and information theory (robert m gray)

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1、EntropyandInformationTheoryiiEntropyandInformationTheoryRobertM.GrayInformationSystemsLaboratoryElectricalEngineeringDepartmentStanfordUniversitySpringer-VerlagNewYorkivThisbookwaspreparedwithLATEXandreproducedbySpringer-Verlagfromcamera-readycopysuppliedbytheauthor.°c1990bySpringerVe

2、rlagvtoTim,Lori,Julia,Peter,Gus,AmyElizabeth,andAliceandinmemoryofTinoviContentsProloguexi1InformationSources11.1Introduction..............................11.2ProbabilitySpacesandRandomVariables.............11.3RandomProcessesandDynamicalSystems............51.4Distributions...........

3、..................61.5StandardAlphabets.........................101.6Expectation..............................111.7AsymptoticMeanStationarity...................141.8ErgodicProperties..........................152EntropyandInformation172.1Introduction..............................172.2E

4、ntropyandEntropyRate.....................172.3BasicPropertiesofEntropy.....................202.4EntropyRate.............................312.5ConditionalEntropyandInformation...............352.6EntropyRateRevisited.......................412.7RelativeEntropyDensities....................

5、..443TheEntropyErgodicTheorem473.1Introduction..............................473.2StationaryErgodicSources.....................503.3StationaryNonergodicSources...................563.4AMSSources.............................593.5TheAsymptoticEquipartitionProperty..............634Informat

6、ionRatesI654.1Introduction..............................654.2StationaryCodesandApproximation...............654.3InformationRateofFiniteAlphabetProcesses..........73viiviiiCONTENTS5RelativeEntropy775.1Introduction..............................775.2Divergence............................

7、..775.3ConditionalRelativeEntropy....................925.4LimitingEntropyDensities.....................1045.5InformationforGeneralAlphabets.................1065.6SomeConvergenceResults......................1166InformationRatesII1196.1Introduction..............................1196.2Inf

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