Information Theory by Yao Xie
This note will explore the basic concepts of information theory. It is highly recommended for students planning to delve into the fields of communications, data compression, and statistical signal processing. Topics covered includes: Entropy and mutual information, Chain rules and inequalities, Data processing, Fano's inequality, Asymptotic equipartition property, Entropy rate, Source coding and Kraft inequality, Optimal code length and roof code, Huffman codes, Shannon-Fano-Elias and arithmetic codes, Maximum entropy, Channel capacity, Channel coding theorem, Differential entropy, Gaussian channel, Parallel Gaussian channel and water-filling, Quantization and rate-distortion.
Author(s): Yao Xie
NA 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 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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