Lecture Notes on Information Theory by Prof. Dr. rer. nat. Rudolf Mathar

An Introduction to Information Theory and Applications

By F. Bavaud, J. C. Chappelier, and J. Kohlas—This long note contains a good survey of information theory and its applications. It introduces the basic ideas of uncertainty and information, then also the more practical extensions such as optimal coding schemes, followed by the theories underlying versions of stationary processes and Markov chains. Other challenges, as the note addresses, pertain to noisy transmission environments in coding. Highlighted here are several advanced topics that follow, including, importantly, error-correcting codes and cryptography. The resource will give both a theoretical background and a practical overview of how to encode, transmit, and secure information effectively. It is a very important guide for those who seek a deep understanding of information theory and how it relates to real problems of communication and data processing.

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

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 Entropy

Om Carter-Introduction to information theory and entropy: It goes in deep to do some basic concepts of information theory, focusing on the concept of entropy and its applications. It does so by first investigating the measure of complexity and the elementary theories of probability before introducing some key ideas in information theory. It ranges from basic issues, such as entropy theory and the Gibbs inequality, up to Shannon's communication theory but also to practical applications in many diversified fields. Other topics dealt with are Bayes Theorem, analog channels, the Maximum Entropy Principle, and applications to biology and physics. The Kullback-Leibler information measure will be discussed in trying to cast light upon quantification of information and its relations with different fields of science. This book should be ideal for the general reader interested in information theory and its immense areas of application..

Author(s): Tom Carter

139 Pages

Information Theory for Data Communications and Processing

This is a wide-ranging text by Shlomo Shamai and Abdellatif Zaidi, covering both foundational and advanced topics in information theory applied to data communications and processing. It discusses basic issues, such as information bottleneck problems, unsupervised clustering via methods of the variational information bottleneck, and rate-distortion analysis. It proceeds to get into subjects of a higher level of difficulty: non-orthogonal eMBB and URLLC radio access, robust baseband compression techniques, and amplitude-constrained MIMO channels. Efficient algorithms have been derived for multicasting, content placement in cache networks, and the fundamental limits of caching. The title will be a ready reference for researchers and practitioners interested in the theory and practice of modern communication systems, comprehensively covering recent advancement efforts and applications in information theory.

Author(s): Shlomo Shamai, Abdellatif Zaidi

296 Pages

Information Theory and its applications in theory of computation

This set of lecture notes by Venkatesan Guruswami and Mahdi Cheraghchi addresses the intersection of information theory and theoretical computer science. The core topics to be covered in the lecture note include entropy, Kraft's inequality, source coding theorem, conditional entropy, and mutual information. It also covers KL-divergence, Chernoff bounds, data processing, and Fano's inequalities. Key concepts include AEP, universal source coding using the Lempel-Ziv algorithm, and proof of its optimality. It covers discrete channels and channel capacity, the Noisy Channel Coding Theorem, and how to construct capacity-achieving codes by concatenation and by polar codes. Additional topics: Bregman's theorem, Shearer's Lemma, graph entropy, and applications to optimal set disjointness lower bounds. This text offers a wide-ranging view of how the basic principles of information theory shed light on the construction of algorithms, and the establishment of bounds-on the complexity of problems in the field of theoretical computation.

Author(s): Venkatesan Guruswami and Mahdi Cheraghchi

NA Pages