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 
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
Lecture Notes on Information Theory by Prof. Dr. rer. nat. Rudolf Mathar
The lecture notes of Prof. Dr. rer. nat. Rudolf Mathar give a clear and very compact introduction into information theory. These notes are divided into three key parts: the basics of information theory, source coding, and information channels. The introduction treats the basic notions and definitions in information theory in a very solid way. Source coding gives methods and different techniques that are used in encoding information, while the information channels section discusses the pattern in which information is carried and noise that affects it. This resource is a good pick for students and professionals who seek structure in the principles of information theory and its applications from a respected expert in the field.
Author(s): Prof. Dr. rer. nat. Rudolf Mathar, Institute for Theoretical Information Technology Kopernikusstr, Germany
59 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
It serves as a basis for everything, from the very basics of thermodynamics and information theory to thermodynamic potentials and distributions, principles of irreversibility, phase space evolution, and beyond. The book informs the readers about the very basics of information theory: basic notions, basic definitions, and applications. It also offers a fresh perspective on the second law of thermodynamics and quantum information, and insights into the modern view of how information theory is intertwined with the laws of physics. This book will be very useful to anyone who wants to gain an understanding of the basic issues in both thermodynamics and information theory and their intersection in current usage.
Author(s): Gregory Falkovich
165 Pages
Information Theory Lecture Notes
Prof. Tsachy Weissman's lecture notes are an excellent summary of the core topics in the subject of information theory. The document initiates with a basic overview of entropy and relative entropy, followed by mutual information and asymptotic equipartition property. Further, it discusses communications theory, channel capacity, and the method of types. It also covers key topics such as typicality-conditioned and joint, lossy compression, and rate-distortion theory. The notes also include joint source-channel coding, where there is quite a good grasp of the principles and applications of information theory. These notes will be very helpful for students and professionals looking forward to structured, comprehensive knowledge about the subject.
Author(s): Prof. Tsachy Weissman
75 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
