Information Theory by Yao Xie

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 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

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

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