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Information Theory and its applications in theory of computation
This note covers the following topics: Entropy, Kraft's inequality, Source coding theorem, conditional entropy, mutual information, KL-divergence and connections, KL-divergence and Chernoff bounds, Data processing and Fano's inequalities, Asymptotic Equipartition Property, Universal source coding: Lempel-Ziv algorithm and proof of its optimality, Source coding via typical sets and universality, joint typicality and joint AEP, discrete channels and channel capacity, Proof of Noisy channel coding theorem, Constructing capacity-achieving codes via concatenation, Polarization, Arikan's recursive construction of a polarizing invertible transformation, Polar codes construction, Bregman's theorem, Shearer's Lemma and applications, Source coding and Graph entropy, Monotone formula lower bounds via graph entropy, Optimal set Disjointness lower bound and applications, Compression of arbitrary communication protocols, Parallel repetition of 2-prover 1-round games.
Author(s): Venkatesan Guruswami and Mahdi Cheraghchi
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Applied Digital Information theory
This note serves as a comprehensive guide to fundamental concepts in information theory and coding. This pdf provides discrete probability theory, information theory, and coding principles. Beginning with Shannon's measure of information, then delves into the efficient coding of information, the methodology of typical sequences is introduced, emphasizing the distinction between lossy and lossless source encoding. The text also discusses coding for noisy digital channels, block coding principles and tree and trellis coding principles.
Author(s): James L.Massey
153 Pages
This book explains basics of thermodynamics, including thermodynamic potentials, microcanonical and canonical distributions, and evolution in the phase space, The inevitability of irreversibility, basics of information theory, applications of information theory, new second law of thermodynamics and quantum information.
Author(s): Gregory Falkovich
165 Pages
Information Theory Lecture Notes
This PDF covers the following topics related to Information Theory : Introduction, Entropy, Relative Entropy, and Mutual Information, Asymptotic Equipartition Properties, Communication and Channel Capacity, Method of Types, Conditional and Joint Typicality, Lossy Compression & Rate Distortion Theory, Joint Source Channel Coding.
Author(s): Prof. Tsachy Weissman
75 Pages
Information Theory by Y. Polyanskiy
This PDF covers the following topics related to Information Theory : Information measures, Lossless data compression, Binary hypothesis testing, Channel coding, Lossy data compression, Advanced topics.
Author(s): Y. Polyanskiy, Y. Wu
295 Pages
Information Theory and Coding cam
The PDF covers the following topics related to Information Theory : Foundations: probability, uncertainty, information, Entropies defined, and why they are measures of information, Source coding theorem; prefix, variable-, and fixed-length codes, Channel types, properties, noise, and channel capacity, Continuous information, density, noisy channel coding theorem, Fourier series, convergence, orthogonal representation, Useful Fourier theorems, transform pairs, Sampling, aliasing, Discrete Fourier transform, Fast Fourier Transform Algorithms, The quantised degrees-of-freedom in a continuous signal, Gabor-Heisenberg-Weyl uncertainty relation, Kolmogorov complexity.
Author(s): J G Daugman
75 Pages
Information Theory in Computer Science
This note explains the following topics: Shearer's Lemma, Entropy, Relative Entropy, Hypothesis testing, total variation distance and Pinsker's lemma, Stability in Shearer's Lemma, Communication Complexity, Set Disjointness, Direct Sum in Communication Complexity and Internal Information Complexity, Data Structure Lower Bounds via Communication Complexity, Algorithmic Lovasz Local Lemma, Parallel Repetition Theorem, Graph Entropy and Sorting.
Author(s): Madhu Sudan
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