Author : Maxim Raginsky
Publisher :
Page : 256 pages
File Size : 50,87 MB
Release : 2014
Category : Computers
ISBN : 9781601989062
Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.
Author : Maxim Raginsky
Publisher :
Page : 247 pages
File Size : 17,31 MB
Release : 2018
Category : Concentration functions
ISBN : 9781680835359
Concentration inequalities have been the subject of exciting developments during the last two decades, and have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, mathematical statistics, pure and applied probability theory (e.g., concentration of measure phenomena in random graphs, random matrices, and percolation), information theory, theoretical computer science, learning theory, and dynamical systems. This monograph focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. In addition to being a survey, this monograph also includes various new recent results derived by the authors.
Author : Stéphane Boucheron
Publisher : Oxford University Press
Page : 492 pages
File Size : 25,52 MB
Release : 2013-02-07
Category : Mathematics
ISBN : 0199535256
Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.
Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 46,40 MB
Release : 2018-09-27
Category : Business & Economics
ISBN : 1108415199
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author : Imre Csiszár
Publisher : Now Publishers Inc
Page : 128 pages
File Size : 20,9 MB
Release : 2004
Category : Computers
ISBN : 9781933019055
Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.
Author : Thomas M. Cover
Publisher : John Wiley & Sons
Page : 788 pages
File Size : 21,22 MB
Release : 2012-11-28
Category : Computers
ISBN : 1118585771
The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.
Author : Devdatt P. Dubhashi
Publisher : Cambridge University Press
Page : 213 pages
File Size : 15,62 MB
Release : 2009-06-15
Category : Computers
ISBN : 1139480995
Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff–Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff–Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.
Author : Abbas El Gamal
Publisher : Cambridge University Press
Page : 666 pages
File Size : 43,88 MB
Release : 2011-12-08
Category : Technology & Engineering
ISBN : 1139503146
This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.
Author : John Watrous
Publisher :
Page : 599 pages
File Size : 39,9 MB
Release : 2018-04-26
Category : Computers
ISBN : 1107180562
Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.
Author : Eric Carlen
Publisher : Springer
Page : 620 pages
File Size : 37,64 MB
Release : 2017-04-20
Category : Mathematics
ISBN : 1493970054
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.
