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Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
Published: 1957-01-01
Total Pages: 130
ISBN-13: 0486604349
DOWNLOAD EBOOKFirst comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author: David Ellerman
Publisher: Springer Nature
Published: 2021-10-30
Total Pages: 121
ISBN-13: 3030865525
DOWNLOAD EBOOKThis monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.
Author: Amiel Feinstein
Publisher:
Published: 1958
Total Pages: 160
ISBN-13:
DOWNLOAD EBOOKAuthor: George J. Klir
Publisher: John Wiley & Sons
Published: 2005-11-22
Total Pages: 499
ISBN-13: 0471755567
DOWNLOAD EBOOKDeal with information and uncertainty properly and efficientlyusing tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized InformationTheory contains comprehensive and up-to-date coverage of resultsthat have emerged from a research program begun by the author inthe early 1990s under the name "generalized information theory"(GIT). This ongoing research program aims to develop a formalmathematical treatment of the interrelated concepts of uncertaintyand information in all their varieties. In GIT, as in classicalinformation theory, uncertainty (predictive, retrodictive,diagnostic, prescriptive, and the like) is viewed as amanifestation of information deficiency, while information isviewed as anything capable of reducing the uncertainty. A broadconceptual framework for GIT is obtained by expanding theformalized language of classical set theory to include moreexpressive formalized languages based on fuzzy sets of varioustypes, and by expanding classical theory of additive measures toinclude more expressive non-additive measures of varioustypes. This landmark book examines each of several theories for dealingwith particular types of uncertainty at the following fourlevels: * Mathematical formalization of the conceived type ofuncertainty * Calculus for manipulating this particular type ofuncertainty * Justifiable ways of measuring the amount of uncertainty in anysituation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complexmaterial and demonstrate practical applications, generoushistorical and bibliographical notes, end-of-chapter exercises totest readers' newfound knowledge, glossaries, and an Instructor'sManual, this is an excellent graduate-level textbook, as well as anoutstanding reference for researchers and practitioners who dealwith the various problems involving uncertainty and information. AnInstructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.
Author: A. Ya. Khinchin
Publisher: Courier Corporation
Published: 2013-04-09
Total Pages: 130
ISBN-13: 0486318443
DOWNLOAD EBOOKFirst comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author: Herbert S. Green
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 248
ISBN-13: 364257162X
DOWNLOAD EBOOKIn this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.
Author: Christopher G. Timpson
Publisher: Oxford Philosophical Monograph
Published: 2013-04-25
Total Pages: 308
ISBN-13: 0199296464
DOWNLOAD EBOOKChristopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.
Author: JV Stone
Publisher: Sebtel Press
Published: 2015-01-01
Total Pages: 243
ISBN-13: 0956372856
DOWNLOAD EBOOKOriginally developed by Claude Shannon in the 1940s, information theory laid the foundations for the digital revolution, and is now an essential tool in telecommunications, genetics, linguistics, brain sciences, and deep space communication. In this richly illustrated book, accessible examples are used to introduce information theory in terms of everyday games like ‘20 questions’ before more advanced topics are explored. Online MatLab and Python computer programs provide hands-on experience of information theory in action, and PowerPoint slides give support for teaching. Written in an informal style, with a comprehensive glossary and tutorial appendices, this text is an ideal primer for novices who wish to learn the essential principles and applications of information theory.
Author: Imre Csiszár
Publisher: Now Publishers Inc
Published: 2004
Total Pages: 128
ISBN-13: 9781933019055
DOWNLOAD EBOOKInformation 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: Marco Tomamichel
Publisher: Springer
Published: 2015-10-14
Total Pages: 146
ISBN-13: 3319218913
DOWNLOAD EBOOKThis book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
