Information Theory

This note covers the following topics, Entropy, Krafts inequality, Source coding theorem, conditional entropy, mutual information, KLdivergence and connections, KLdivergence and Chernoff bounds, Data processing and Fanos inequalities, Asymptotic Equipartition Property, Universal source coding, LempelZiv 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 capacityachieving codes via concatenation, Polarization, Arikans recursive construction of a polarizing invertible transformation, Polar codes construction, Bregmans theorem, Shearers 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 2prover 1round games.

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 fixedlength 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 degreesoffreedom in a continuous signal, GaborHeisenbergWeyl uncertainty relation, Kolmogorov complexity.

The PDF covers the following topics related to Information Theory, Information Theory for Data Communications and Processing, On the Information Bottleneck Problems, Models, Connections,Applications and Information Theoretic Views, Variational Information Bottleneck for Unsupervised Clustering, Deep Gaussian Mixture Embedding, Asymptotic RateDistortion Analysis of Symmetric Remote Gaussian Source Coding, Centralized Encoding vs. Distributed Encoding, NonOrthogonal eMBBURLLC Radio Access for Cloud Radio Access Networks with Analog Fronthauling, Robust Baseband Compression Against Congestion in PacketBased Fronthaul Networks Using Multiple Description Coding, Amplitude Constrained MIMO Channels, Properties of Optimal Input Distributions and Bounds on the Capacity, QuasiConcavity for Gaussian Multicast Relay Channels, Gaussian Multiple Access Channels with OneBit Quantizer at the Receiver, Efficient Algorithms for Coded Multicasting in Heterogeneous Caching Networks, CrossEntropy Method for Content Placement and User Association in CacheEnabled Coordinated UltraDense Networks, Symmetry, Outer Bounds, and Code Constructions, A ComputerAided Investigation on the Fundamental Limits of Caching.

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 and Rate Distortion Theory, Joint Source Channel Coding.

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.

This note covers Measuring complexity, Some probability ideas, Basics of information theory, Some entropy theory, The Gibbs inequality, A simple physical example Shannons communication theory, Application to Biology, Examples using Bayes Theorem, Analog channels, A Maximum Entropy Principle, Application to Physics lasers, KullbackLeibler information measure.

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, LeCams and Fanos 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, subGaussian and subexponential random variables, martingale methods, uniformity covering topics such as KullbackLeibler divergence, PACBayes bounds, interactive data analysis, and error bounds.

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 Shannons 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.

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.

This book contains below topics, Introduction to information theory, Probability, entropy, and inference, Source coding, Noisy channel coding, Sparse graph codes, Bayesian inference and Monte Carlo methods, Neural networks, Decision theory.