作者：陈杰[等]编著
页数：153
出版社：北京航空航天大学出版社
出版日期：2016
ISBN：9787512419728
电子书格式：pdf/epub/txt
内容简介
Thisbooksystematicallyintroducedthefundamentalsofinformationtheory,focusingonthebasicmodelofcommunicationsystems．Itconsistsof11Chapters,includingtwoparts,namely,basicconceptionsofinforＧmationtheoryandrelatedapplicationsofinformationtheory．Thefirstpartcontainsstatisticalmeasureofinformation,discretesource,losslesssourcecodinganddatacompression,discretechannelanditscapacity,channelcoding,whilethesecondpartincludesratedistortion,continuoussource,continuouschannelanditscapacity,maximumentropyandspectrumestimationaswellascomputersimulationexperimentsrelevanttoinformationtheory． Thisbooksummarizedtheexperienceoftheauthorsonteachinginformationcoursein EnglishandChinese,togetherwiththeirunderstandingsfromyearsscientificresearchpractice．Itcanbeusedasteachingmaterialoninformationtheorycourseforbothinternationalundergraduateandgraduatestudents．
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
