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1、InformationTheoryandCodingComputerScienceTriposPartII,MichaelmasTerm11LecturesbyJGDaugman1.Foundations:Probability,Uncertainty,andInformation2.EntropiesDe ned,andWhytheyareMeasuresofInformation3.SourceCodingTheorem;Pre x,Variable-,&Fixed-LengthCodes4.ChannelTypes,Properti
2、es,Noise,andChannelCapacity5.ContinuousInformation;Density;NoisyChannelCodingTheorem6.FourierSeries,Convergence,OrthogonalRepresentation7.UsefulFourierTheorems;TransformPairs;Sampling;Aliasing8.DiscreteFourierTransform.FastFourierTransformAlgorithms9.TheQuantizedDegrees-o
3、f-FreedominaContinuousSignal10.Gabor-Heisenberg-WeylUncertaintyRelation.OptimalLogons"11.KolmogorovComplexityandMinimalDescriptionLengthInformationTheoryandCodingJGDaugmanPrerequisitecourses:Probability;MathematicalMethodsforCS;DiscreteMathematicsAimsTheaimsofthiscoursea
4、retointroducetheprinciplesandapplicationsofinformationtheory.Thecoursewillstudyhowinformationismeasuredintermsofprobabilityandentropy,andtherelationshipsamongconditionalandjointentropies;howtheseareusedtocalculatethecapacityofacommunicationchannel,withandwithoutnoise;codi
5、ngschemes,includingerrorcorrectingcodes;howdiscretechannelsandmeasuresofinformationgeneralisetotheircontinuousforms;theFourierperspective;andextensionstowavelets,complexity,compression,andecientcodingofaudio-visualinformation.LecturesFoundations:probability,uncertainty,
6、information.Howconceptsofrandomness,redundancy,compressibility,noise,bandwidth,anduncertaintyarerelatedtoinformation.Ensembles,randomvariables,marginalandconditionalprobabilities.Howthemetricsofinformationaregroundedintherulesofprobability.Entropiesde ned,andwhytheyareme
7、asuresofinformation.Marginalentropy,jointentropy,conditionalentropy,andtheChainRuleforentropy.Mutualinformationbetweenensemblesofrandomvariables.Whyentropyisthefundamentalmeasureofinfor-mationcontent.Sourcecodingtheorem;pre x,variable-,and xed-lengthcodes.Symbolcodes.The
8、binarysymmetricchannel.Capacityofanoiselessdiscretechannel.Errorcorrectingcodes.Channeltypes,pr
