Lecture Notes on statistics and information Theory
This lecture note navigates through information theory, statistics and measure theory. It covers fundamental concepts such as definitions, chain rules, data processing inequalities, and divergences and extends to optimal procedures, LeCam’s and Fano’s inequalities, and operational results like entropy and source coding. It also focus on exponential families and statistical modeling, fitting procedures, and lower bounds on testing parameters, sub-Gaussian and sub-exponential random variables, martingale methods, uniformity covering topics such as Kullback-Leibler divergence, PAC-Bayes bounds, interactive data analysis, and error bounds.
Author(s): John Duchi
464 Pages 
An Introduction to Information Theory and Applications
This note explains the following topics: uncertainty and information, Efficient coding of information, Stationary processes and markov chains, Coding for noisy transmission, Complements to efficient coding of Information, Error correcting codes and cryptography.
Author(s): F Bavaud, J C Chappelier and J Kohlas
293 Pages
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
An introduction to information Theory and Entropy
This note covers Measuring complexity, Some probability ideas, Basics of information theory, Some entropy theory, The Gibbs inequality, A simple physical example Shannon’s communication theory, Application to Biology, Examples using Bayes Theorem, Analog channels, A Maximum Entropy Principle, Application to Physics(lasers), Kullback-Leibler information measure.
Author(s): Tom Carter
139 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 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
NA Pages
