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Concentration of Measure Inequalities in Information Theory, Communications, and Coding

Author: Maxim Raginsky

Publisher:

Published: 2014

Total Pages: 256

ISBN-13: 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.

Concentration of Measure Inequalities in Information Theory, Communications, and Coding: ThirdEdition

Author: Maxim Raginsky

Publisher: Foundations and Trends (R) in Communications and Information Theory

Published: 2018-12-18

Total Pages: 266

ISBN-13: 9781680835342

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This book 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.

Concentration Inequalities

Author: Stéphane Boucheron

Publisher: Oxford University Press

Published: 2013-02-07

Total Pages: 492

ISBN-13: 0199535256

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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.

Convexity and Concentration

Author: Eric Carlen

Publisher: Springer

Published: 2017-04-20

Total Pages: 626

ISBN-13: 1493970054

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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.

Mathematics Going Forward

Author: Jean-Michel Morel

Publisher: Springer Nature

Published: 2023-06-14

Total Pages: 629

ISBN-13: 3031122445

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This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Digital Quantum Information Processing with Continuous-Variable Systems

Author: Takaya Matsuura

Publisher: Springer Nature

Published: 2023-02-06

Total Pages: 172

ISBN-13: 9811982880

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The book provides theoretical methods of connecting discrete-variable quantum information processing to continuous-variable one. It covers the two major fields of quantum information processing, quantum communication and quantum computation, leading to achievement of a long-sought full security of continuous-variable quantum key distribution (QKD) and proposal of a resource-efficient method for optical quantum computing. Firstly, the book provides a security of continuous-variable QKD against arbitrary attacks under a realistic condition such as finite communication rounds and the use of digitized information processing. The book also provides the unified view for conventionally used approximate Gottesman-Kitaev-Preskill (GKP) codes, which encodes qudits on a continuous-variable system, enabling direct comparison between researches based on different approximations. The book finally proposes a resource-efficient method to realize the universal optical quantum computation using the GKP code via the direct preparation of the GKP magic state instead of GKP Pauli states. Feasibility of the proposed protocol is discussed based on the existing experimental proposals for the GKP state preparation.

Information Theory and Statistics

Author: Imre Csiszár

Publisher: Now Publishers Inc

Published: 2004

Total Pages: 128

ISBN-13: 9781933019055

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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.

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Quantum Information Theory

Author: Mark Wilde

Publisher: Cambridge University Press

Published: 2013-04-18

Total Pages: 673

ISBN-13: 1107034256

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A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.

An Introduction to Single-User Information Theory

Author: Fady Alajaji

Publisher: Springer

Published: 2018-04-24

Total Pages: 323

ISBN-13: 9811080011

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This book presents a succinct and mathematically rigorous treatment of the main pillars of Shannon’s information theory, discussing the fundamental concepts and indispensable results of Shannon’s mathematical theory of communications. It includes five meticulously written core chapters (with accompanying problems), emphasizing the key topics of information measures; lossless and lossy data compression; channel coding; and joint source-channel coding for single-user (point-to-point) communications systems. It also features two appendices covering necessary background material in real analysis and in probability theory and stochastic processes. The book is ideal for a one-semester foundational course on information theory for senior undergraduate and entry-level graduate students in mathematics, statistics, engineering, and computing and information sciences. A comprehensive instructor’s solutions manual is available.