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Information Theory and Coding - University of Cambridge

InformationTheoryandCodingComputerScienc eTripos PartII, MichaelmasTerm11 Lecturesby J G Daugman1. Foundations:Probability, Uncertainty, andInformation2. EntropiesDe ned,andWhy theyareMeasuresof Information3. SourceCodingTheorem;Pre x,Variable-,& Fixed-LengthCodes4. ChannelTypes,Properties,Noise,andChannel Capacity5. ContinuousInformation;Density; NoisyChannelCodingTheorem6. FourierSeries,Convergence,OrthogonalRepr esentation7. UsefulFourierTheorems;TransformPairs;Sam pling;Aliasing8. TheQuantizedDegrees-of-Freedomin a \Logons" Complexity andMinimalDescriptionLengthInformationTh eoryandCodingJ G DaugmanPrerequisitecourses:Probability;M athematical Methods forCS;DiscreteMathematicsAimsTheaimsof thiscourseareto introducetheprinciplesandapplicationsof informationis measuredin termsof probability andentropy, andtherelationshipsamongconditionalandjo int entropies;how theseareusedto calculatethecapacityof a communicationchannel,withandwithoutnoise ;codingschemes,includingerrorcorrectingc odes;how discretechannelsandmeasuresof informationgeneraliseto theircontinuousforms;theFourierperspecti ve; andextensionsto wavelets,complexity, compression,ande cient codingof Foundations:probability, uncertainty, conceptsof randomness,redundancy.

Gabor-Heisenberg-Weyl uncertainty relation. Optimal \Logons". Uni cation of the time-domain and the frequency-domain as endpoints of a continuous deformation. The Uncertainty Principle and its optimal solution by Gabor’s expansion basis of \logons". Multi-resolution wavelet codes. Extension to images, for analysis and compression. Kolmogorov ...

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