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[美] 科沃 (Thomas M.Cover)、[美] 托马斯 (Joy A.Thomas) 著 / 清华大学出版社 / 2003-11 / 平装
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上书时间2020-11-21
信息论基础
《信息论基础》系统介绍了信息论基本原理及其在通信理论、统计学、计算机科学、概率论以及投资理论等领域的应用。作者以循序渐进的方式,介绍了信息量的基本定义、相对熵、互信息以及他们如何自然地用来解决数据压缩、信道容量、信息率失真、统计假设、网络信息流等问题。除此以外,《信息论基础》还探讨了很多教材中从未涉及的问题,如:
热力学第二定律与马尔可夫链之间的联系
Huffman编码的最优性
数据压缩的对偶性
Lempelziv编码
Kolmogorov复杂性
PorfoII0理论
信息论不等式及其数学结论
《信息论基础》可作为通信、电子、计算机、自动控制、统计、经济等专业高年级本科生和研究生的教材或参考书,也可供相关领域的科研人员和专业技术人员参考。
ThomasM.Cover斯坦福大学电气工程系、统计系教授。曾任IEEE信息论学会主席,现任数理统计研究所研究员、IEEE高级会员。1972年以论文“BroadcastChannels”荣获信息论优秀论文奖,1990年被选为“ShannonLecturer”,这是信息论领域的最高荣誉。最近20年,他致力于信息论和统计学之间的关系。
ListofFigures1IntroductionandPreview1.1Previewofthebook2EntropyRelativeEntropyandMutualInformation2.1Entropy2.2Jointentropyandconditionalentropy2.3Relativeentropyandmutualinformation2.4Relationshipbetweenentropyandmutualinformation2.5Chainrulesforentropy,relativeentropyandmutualinformation2.6Jensen'sinequalityanditsconsequences2.7Thelogsuminequalityanditsapplications2.8Dataprocessinginequality2.9Thesecondlawofthermodynamics2.10Sufficientstatistics2.11Fano'sinequalitySummaryofChapter2ProblemsforChapter2Historicalnotes3TheAsymptoticEquipartitionProperty3.1TheAEP3.2ConsequencesoftheAEP:datacompression3.3HighprobabilitysetsandthetypicalsetSummaryofChapter3ProblemsforChapter3Historicalnotes4EntropyRatesofaStochasticProcess4.1Markovchains4.2Entropyrate4.3Example:Entropyrateofarandomwalkonaweightedgraph4.4HiddenMarkovmodelsSummaryofChapter4ProblemsforChapter4Historicalnotes5DataCompression5.1Examplesofcodes5.2Kraftinequality5.3Optimalcodes5.4Boundsontheoptimalcodelength5.5Kraftinequalityforuniquelydecodablecodes5.6Huffmancodes5.7SomecommentsonHuffmancodes5.8OptimalityofHuffmancodes5.9Shannon-Fano-Eliascoding5.10Arithmeticcoding5.11CompetitiveoptimalityoftheShannoncode5.12GenerationofdiscretedistributionsfromfaircoinsSummaryofChapter5ProblemsforChapter5Historicalnotes6GamblingandDataCompression6.1Thehorserace6.2Gamblingandsideinformation6.3Dependenthorseracesandentropyrate6.4TheentropyofEnglish6.5Datacompressionandgambling6.6GamblingestimateoftheentropyofEnglishSummaryofChapter6ProblemsforChapter6Historicalnotes7KolmogorovComplexity7.1Modelsofcomputation7.2Kolmogorovcomplexity:definitionsandexamples7.3Kolmogorovcomplexityandentropy7.4Kolmogorovcomplexityofintegers7.5Algorithmicallyrandomandincompressiblesequences7.6Universalprobability7.7Thehaltingproblemandthenon·computabilityofKolmogorovcomplexity7.8Q7.9Universalgambling7.10Occam'srazor7.11Kolmogorovcomplexityanduniversalprobability7.12TheKolmogorpySuffcientstatisticSummaryofChapter7ProblemsforChapter7ProblemsforChapter8Historicalnotes8ChannelCapacity8.1Examplesofchannelcapacity8.2Symmetricchannels8.3Propertiesofchannelcapacity8.4Previewofthechannelcodingtheorem8.5Definitions8.6Jointlytypicalsequences8.7Thechannelcodingtheorem8.8Zero.errorcodes8.9Fano'sinequalityandtheconversetothecodingtheorem8.10Equalityintheconversetothechannelcodingtheorem8.11Hammingcodes8.12Feedbackcapacity8.13ThejointsourcechannelcodingtheoremSummaryofChapter8ProblemsforChapter8Historicalnotes9DifferentialEntropy9.1Definitions9.2TheAEPforcontinuousrandomvariables9.3Relationofdifferentialentropytodiscreteentropy9.4Jointandconditionaldifferentialentropy9.5Relativeentropyandmutualinformation9.6Propertiesofdifferentialentropy,relativeentropyandmutualinformation9.7DifferentialentropyboundondiscreteentropySummaryofChapter9ProblemsforChanter9Historicalnotes10TheGaussianChannel10.1TheGaussianchannel:definitions10.2ConversetothecodingtheoremforGaussianchannels10.3Band-limitedchannels10.4ParallelGaussianchannels10.5ChannelswithcoloredGaussiannoise10.6GaussianchannelswithfeedbackSummaryofChapter10ProblemsforChapter10Historicalnotes11MaximumEntropyandSpectralEstimation11.1Maximumentropydistributions11.2Examples11.3Ananomalousmaximumentropyproblem11.4Spectrumestimation11.5EntropyratesofaGaussianprocess11.6Burg'smaximumentropytheoremSummaryofChapter11ProblemsforChapter11Historicalnotes12InformationTheoryandStatistics13RateDistortionTHeory14NetworkInformationTheory15InformationTheoryandtheStcokMarket16InequalitiesinInformationTheoryBibliographyListofSymbolsIndex
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