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ELEMENTSOFINFORMATIONTHEORYSecondEditionTHOMASM.COVERJOYA.THOMASAJOHNWILEY&SONS,INC.,PUBLICATIONELEMENTSOFINFORMATIONTHEORYELEMENTSOFINFORMATIONTHEORYSecondEditionTHOMASM.COVERJOYA.THOMASAJOHNWILEY&SONS,INC.,PUBLICATIONCopyright2006byJohnWiley&Sons,Inc.Allrightsreserved.PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.PublishedsimultaneouslyinCanada.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permission.LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orotherdamages.Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat(317)572-3993orfax(317)572-4002.Wileyalsopublishesitsbooksinavarietyofelectronicformats.