Information Theory by Yao Xie

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

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

Advanced Information Theory notes

The lecture notes Advanced Information Theory Notes by Prof. Dr. sc. techn. Gerhard Kramer cover advanced topics in information theory. Information theory within the context of these notes starts with discrete and continuous random variables to base the student in deeper understandings of complicated scenarios. The key areas include channel coding, important for good data transmission; typical sequences and sets, which are fundamental in the theoretical and practical applications of the coding. The text also explores lossy source coding and distributed source coding, which look into how data might be compressed and transmitted with much efficiency. It also covers multiaccess channels, an important aspect in showing just how different sources of data interact. Such a broad-ranging textbook seems particularly suited to readers having a firm grounding in basic information theory, wanting to advance into more advanced areas as well as applications.

Author(s): Prof Dr. sc. techn. Gerhard Kramer

180 Pages

Basics of information theory

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 and Coding cam

This is a PDF document written by J.G. Daugman on the fundamentals of the theory of information and coding. Beginning with the very basic concept of probability and uncertainty, and the concept of information, it arrives at entropies and their meaning. It deals with the source coding theorems: prefix, variable-length, and fixed-length codes. It looks into several kinds of channels, their properties, noise, and channel capacity. The further topics delve into detail with continuous information, noisy channel coding theorems, Fourier series elaborated on in making matters of convergence, orthogonal representation, and useful Fourier theorems. The text also expands into aspects such as sampling and aliasing, DFT, FFT algorithms, and the quantized degrees-of-freedom in continuous signals and concludes with discussions on the Gabor-Heisenberg-Weyl uncertainty relation and Kolmogorov complexity for a general overview of some of the key principles of information theory and coding.

Author(s): J G Daugman

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