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信息理论基础-(英文版)

信息理论基础-(英文版)

出版社:北京航空航天大学出版社出版时间:2016-01-01
开本: 16开 页数: 153
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信息理论基础-(英文版) 版权信息

信息理论基础-(英文版) 内容简介

  Thisbooksystematicallyintroducedthefundamentalsofinformationtheory,focusingonthebasicmodelofcommunicationsystems.Itconsistsof11Chapters,includingtwoparts,namely,basicconceptionsofinforGmationtheoryandrelatedapplicationsofinformationtheory.Thefirstpartcontainsstatisticalmeasureofinformation,discretesource,losslesssourcecodinganddatacompression,discretechannelanditscapacity,channelcoding,whilethesecondpartincludesratedistortion,continuoussource,continuouschannelanditscapacity,maximumentropyandspectrumestimationaswellascomputersimulationexperimentsrelevanttoinformationtheory.  Thisbooksummarizedtheexperienceoftheauthorsonteachinginformationcoursein EnglishandChinese,togetherwiththeirunderstandingsfromyearsscientificresearchpractice.Itcanbeusedasteachingmaterialoninformationtheorycourseforbothinternationalundergraduateandgraduatestudents.

信息理论基础-(英文版) 目录

Chapter1 Introduction ………………………………………………………………………… 1
1.1 Conceptofinformation ………………………………………………………………… 1
1.2 Historyofinformationtheory ………………………………………………………… 2
1.3 Information,messagesandsignals …………………………………………………… 3
1.4 Communicationsystem model ………………………………………………………… 3
1.5 Informationtheoryapplications ……………………………………………………… 4
1.5.1 Electricalengineering(communicationtheory)………………………………… 4
1.5.2 Computerscience(algorithmiccomplexity) …………………………………… 5
Exercises ……………………………………………………………………………………… 5
Chapter2 StatisticalMeasureofInformation ………………………………………………… 6
2.1 Informationofrandomevents ………………………………………………………… 6
2.1.1 SelfGinformation …………………………………………………………………… 6
2.1.2 ConditionalselfGinformation ……………………………………………………… 6
2.1.3 Mutualinformationofevents …………………………………………………… 7
2.2 Informationofdiscreterandomvariables …………………………………………… 8
2.2.1 Entropyofdiscreterandomvariables …………………………………………… 8
2.2.2 Jointentropy……………………………………………………………………… 11
2.2.3 Conditionalentropy ……………………………………………………………… 11
2.2.4 Mutualinformationofdiscreterandomvariables …………………………… 11
2.3 Relationshipbetweenentropyandmutualinformation …………………………… 11
2.4 Mutualinformationandentropyofcontinuousrandomvariables………………… 12
2.4.1 Mutualinformationofcontinuousrandomvariables ………………………… 12
2.4.2 Entropyofcontinuousrandomvariables ……………………………………… 13
Exercises ……………………………………………………………………………………… 14
Chapter3 DiscreteSourceandItsEntropyRate …………………………………………… 15
3.1 Mathematicalmodelofsource ……………………………………………………… 15
3.1.1 Discretesourceandcontinuoussource ………………………………………… 16
3.1.2 Simplediscretesourceanditsextension ……………………………………… 17
3.1.3 Memorylesssourceandsourcewithmemory ………………………………… 18
3.2 Discretememorylesssource ………………………………………………………… 18
3.2.1 Definition ………………………………………………………………………… 18
3.2.2 Extensionofdiscretesource …………………………………………………… 19
3.3 Discretestationarysource …………………………………………………………… 20
3.3.1 Definition ………………………………………………………………………… 20
3.3.2 Entropyrateofdiscretestationarysource …………………………………… 21
3.4 DiscreteMarkovsource ……………………………………………………………… 24
3.4.1 Markovchain …………………………………………………………………… 24
3.4.2 Transitionprobability …………………………………………………………… 25
3.4.3 Markovsourceanditsentropyrate …………………………………………… 28
Exercises ……………………………………………………………………………………… 31
Chapter4 LosslessSourceCodingandDataCompression ………………………………… 33
4.1 Asymptoticequipartitionpropertyandtypicalsequences ………………………… 33
4.2 Losslesssourcecoding ……………………………………………………………… 34
4.2.1 Encoder …………………………………………………………………………… 34
4.2.2 Blockcode ………………………………………………………………………… 35
4.2.3 Fixedlengthcode………………………………………………………………… 36
4.2.4 Variablelengthcode …………………………………………………………… 42
4.3 Datacompression ……………………………………………………………………… 48
4.3.1 Shannoncoding ………………………………………………………………… 49
4.3.2 Huffmancoding ………………………………………………………………… 50
4.3.3 Fanocoding ……………………………………………………………………… 52
Exercises ……………………………………………………………………………………… 52
Chapter5 DiscreteChannelandItsCapacity ……………………………………………… 54
5.1 Mathematicalmodelofchannel ……………………………………………………… 54
5.2 Discretememorylesschannel ………………………………………………………… 55
5.2.1 Mathematicalmodelofdiscretememorylesschannel ………………………… 55
5.2.2 SimpleDMC ……………………………………………………………………… 56
5.2.3 Extensionofdiscretememorylesschannel …………………………………… 60
5.3 Channelcombination ………………………………………………………………… 65
5.4 Channelcapacity ……………………………………………………………………… 70
5.4.1 Conceptofchannelcapacity …………………………………………………… 70
5.4.2 Channelcapacityofseveralspecialdiscretechannels ………………………… 71
5.4.3 Channelcapacityofsymmetricchannels ……………………………………… 73
5.4.4 ChannelcapacityofextendedDMC …………………………………………… 75
5.4.5 ChannelcapacityofindependentparallelDMC ……………………………… 76
5.4.6 Channelcapacityofthesumchannel…………………………………………… 77
5.4.7 Channelcapacityofgeneraldiscretechannels ………………………………… 78
Exercises ……………………………………………………………………………………… 79
Chapter6 NoisyGchannelCoding ……………………………………………………………… 81
6.1 Probabilityoferror …………………………………………………………………… 81
6.2 Decodingrules ………………………………………………………………………… 83
6.3 Channelcoding ………………………………………………………………………… 84
6.3.1 Simplerepetitioncode …………………………………………………………… 84
6.3.2 Linearcode ……………………………………………………………………… 87
6.4 NoisyGchannelcodingtheorem ……………………………………………………… 91
Exercises ……………………………………………………………………………………… 91
Chapter7 RateDistortion …………………………………………………………………… 93
7.1 Quantization …………………………………………………………………………… 93
7.2 Distortiondefinition…………………………………………………………………… 94
7.2.1 Distortionfunction ……………………………………………………………… 94
7.2.2 MeanGdistortion ………………………………………………………………… 95
7.3 Ratedistortionfunction ……………………………………………………………… 97
7.3.1 Fidelitycriterionforgivenchannel …………………………………………… 97
7.3.2 Definitionofratedistortionfunction…………………………………………… 98
7.3.3 Propertyofratedistortionfunction …………………………………………… 98
7.4 Ratedistortiontheoremandtheconverse ………………………………………… 101
7.5 Thecalculationofratedistortionfunction ………………………………………… 103
Exercises …………………………………………………………………………………… 105
Chapter8 ContinuousSourceandItsEntropyRate ……………………………………… 107
8.1 Continuoussource …………………………………………………………………… 107
8.2 Entropyofcontinuoussource ……………………………………………………… 107
8.3 Maximumentropyofcontinuoussource…………………………………………… 109
8.4 Jointentropy,conditionalentropyandmutualinformationforcontinuous
randomvariables …………………………………………………………………… 109
8.5 Entropyrateofcontinuoussource ………………………………………………… 111
8.6 Ratedistortionforcontinuoussource ……………………………………………… 114
Exercises …………………………………………………………………………………… 117
Chapter9 ContinuousChannelandItsCapacity …………………………………………… 119
9.1 Capacityofcontinuouschannel …………………………………………………… 119
9.1.1 CapacityofdiscreteGtimechannel……………………………………………… 119
9.1.2 CapacityofcontinuousGtimechannel ………………………………………… 120
9.2 TheGaussianchannel ……………………………………………………………… 121
9.3 BandGlimitedchannels ……………………………………………………………… 122
9.4 Codingtheoremforcontinuouschannel …………………………………………… 123
Exercises …………………………………………………………………………………… 124
Chapter10 MaximumEntropyandSpectrumEstimation ………………………………… 125
10.1 Maximumentropyprobabilitydistribution ……………………………………… 125
10.1.1 Maximumentropydistribution ……………………………………………… 125
10.1.2 Examples ……………………………………………………………………… 126
10.2 Maximumentropyspectrumestimation ………………………………………… 127
10.2.1 Burgsmaxentropytheorem ………………………………………………… 127
10.2.2 Maximumentropyspectrumestimation …………………………………… 130
Exercises …………………………………………………………………………………… 137
Chapter11 ExperimentsofInformationTheory …………………………………………… 138
11.1 Measureofinformation …………………………………………………………… 138
11.1.1 Informationcalculator ………………………………………………………… 138
11.1.2 Propertiesofentropy ………………………………………………………… 139
11.2 SimulationofMarkovsource ……………………………………………………… 140
11.3 Performancesimulationforsourcecoding ……………………………………… 141
11.3.1 Shannoncoding ……………………………………………………………… 142
11.3.2 Huffmancoding ……………………………………………………………… 143
11.3.3 Fanocoding …………………………………………………………………… 144
11.4 SimulationofBSC ………………………………………………………………… 144
11.5 Simulationofthecascadechannel ………………………………………………… 145
11.6 Calculationofchannelcapacity …………………………………………………… 148
11.7 Decodingrules ……………………………………………………………………… 149
11.8 Performancedemonstrationofchannelcoding…………………………………… 150
References ……………………………………………………………………………………… 152
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