Entropy and Information Theory

Author: Robert M. Gray

Publisher: Springer Science & Business Media

ISBN: 9781441979704

Category: Technology & Engineering

Page: 409

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This book is an updated version of the information theory classic, first published in 1990. About one-third of the book is devoted to Shannon source and channel coding theorems; the remainder addresses sources, channels, and codes and on information and distortion measures and their properties. New in this edition: Expanded treatment of stationary or sliding-block codes and their relations to traditional block codes Expanded discussion of results from ergodic theory relevant to information theory Expanded treatment of B-processes -- processes formed by stationary coding memoryless sources New material on trading off information and distortion, including the Marton inequality New material on the properties of optimal and asymptotically optimal source codes New material on the relationships of source coding and rate-constrained simulation or modeling of random processes Significant material not covered in other information theory texts includes stationary/sliding-block codes, a geometric view of information theory provided by process distance measures, and general Shannon coding theorems for asymptotic mean stationary sources, which may be neither ergodic nor stationary, and d-bar continuous channels.

Abstract Methods in Information Theory

Author: Y–ichir“ Kakihara

Publisher: World Scientific

ISBN: 9789810237110

Category: Mathematics

Page: 251

View: 7636

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Information Theory is studied from the following view points: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels. Shannon entropy and Kolmogorov-Sinai entropy are defined and their basic properties are examined, where the latter entropy is extended to be a linear functional on a certain set of measures. Ergodic and mixing properties of stationary sources are studied as well as AMS (asymptotically mean stationary) sources. The main purpose of this book is to present information channels in the environment of real and functional analysis as well as probability theory. Ergodic channels are characterized in various manners. Mixing and AMS channels are also considered in detail with some illustrations. A few other aspects of information channels including measurability, approximation and noncommutative extensions, are also discussed.

Entropy and Information

Author: Mikhail V. Volkenstein

Publisher: Springer Science & Business Media

ISBN: 9783034600781

Category: Science

Page: 210

View: 7061

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This is just...entropy, he said, thinking that this explained everything, and he repeated the strange word a few times. 1 ? Karel Capek , “Krakatit” This “strange word” denotes one of the most basic quantities of the physics of heat phenomena, that is, of thermodynamics. Although the concept of entropy did indeed originate in thermodynamics, it later became clear that it was a more universal concept, of fundamental signi?cance for chemistry and biology, as well as physics. Although the concept of energy is usually considered more important and easier to grasp, it turns out, as we shall see, that the idea of entropy is just as substantial—and moreover not all that complicated. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy. Furthermore, entropy has remarkable properties. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium. Thereis a surprisingconnectionbetween entropyandinformation,thatis,thetotalintelligencecommunicatedbyamessage. All of this is expounded in the present book, thereby conveying informationto the readeranddecreasinghis entropy;butitis uptothe readertodecidehowvaluable this information might be.

Science and Information Theory

Author: Leon Brillouin

Publisher: Courier Corporation

ISBN: 0486497550

Category: Science

Page: 351

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Geared toward upper-level undergraduates and graduate students, this classic resource by a giant of 20th-century mathematics applies principles of information theory to Maxwell's demon, thermodynamics, and measurement problems. 1962 edition.

Elements of Information Theory

Author: Thomas M. Cover,Joy A. Thomas

Publisher: John Wiley & Sons

ISBN: 1118585771

Category: Computers

Page: 792

View: 6413

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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. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

A Student's Guide to Coding and Information Theory

Author: Stefan M. Moser,Po-Ning Chen

Publisher: Cambridge University Press

ISBN: 1107015839

Category: Computers

Page: 191

View: 4862

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A concise, easy-to-read guide, introducing beginners to the engineering background of modern communication systems, from mobile phones to data storage. Assuming only basic knowledge of high-school mathematics and including many practical examples and exercises to aid understanding, this is ideal for anyone who needs a quick introduction to the subject.

Information Theory of Molecular Systems

Author: Roman F. Nalewajski

Publisher: Elsevier

ISBN: 0080459749

Category: Computers

Page: 462

View: 9763

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As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information "distance" (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT), followed by an outline of the main ideas and techniques of IT, including several illustrative applications to molecular systems. Coverage includes information origins of the chemical bond, unbiased definition of molecular fragments, adequate entropic measures of their internal (intra-fragment) and external (inter-fragment) bond-orders and valence-numbers, descriptors of their chemical reactivity, and information criteria of their similarity and independence. Information Theory of Molecular Systems is recommended to graduate students and researchers interested in fresh ideas in the theory of electronic structure and chemical reactivity. ·Provides powerful tools for tackling both classical and new problems in the theory of the molecular electronic structure and chemical reactivity ·Introduces basic concepts of the modern electronic structure/reactivity theory based upon the Density Functional Theory (DFT) ·Outlines main ideas and techniques of Information Theory

Information Theory and Network Coding

Author: Raymond W. Yeung

Publisher: Springer Science & Business Media

ISBN: 0387792333

Category: Computers

Page: 580

View: 9040

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This book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy. The last few years have witnessed the rapid development of network coding into a research ?eld of its own in information science. With its root in infor- tion theory, network coding has not only brought about a paradigm shift in network communications at large, but also had signi?cant in?uence on such speci?c research ?elds as coding theory, networking, switching, wireless c- munications,distributeddatastorage,cryptography,andoptimizationtheory. While new applications of network coding keep emerging, the fundamental - sults that lay the foundation of the subject are more or less mature. One of the main goals of this book therefore is to present these results in a unifying and coherent manner. While the previous book focused only on information theory for discrete random variables, the current book contains two new chapters on information theory for continuous random variables, namely the chapter on di?erential entropy and the chapter on continuous-valued channels. With these topics included, the book becomes more comprehensive and is more suitable to be used as a textbook for a course in an electrical engineering department.

Information Theory in Computer Vision and Pattern Recognition

Author: Francisco Escolano Ruiz,Pablo Suau Pérez,Boyán Ivanov Bonev

Publisher: Springer Science & Business Media

ISBN: 1848822979

Category: Computers

Page: 364

View: 2416

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Information theory has proved to be effective for solving many computer vision and pattern recognition (CVPR) problems (such as image matching, clustering and segmentation, saliency detection, feature selection, optimal classifier design and many others). Nowadays, researchers are widely bringing information theory elements to the CVPR arena. Among these elements there are measures (entropy, mutual information...), principles (maximum entropy, minimax entropy...) and theories (rate distortion theory, method of types...). This book explores and introduces the latter elements through an incremental complexity approach at the same time where CVPR problems are formulated and the most representative algorithms are presented. Interesting connections between information theory principles when applied to different problems are highlighted, seeking a comprehensive research roadmap. The result is a novel tool both for CVPR and machine learning researchers, and contributes to a cross-fertilization of both areas.

Probability Space

Author: Nancy Kress

Publisher: Macmillan

ISBN: 9780765345141

Category: Fiction

Page: 368

View: 7881

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As humans face defeat at the hands of the alien Fallers, four Earth dwellers travel deep into space to test a theory, and hopefully defeat their enemy, in the epic conclusion of the Probability Trilogy, which began with Probability Moon and Probability Sun. Reprint.

Information Theory and Evolution

Author: John Avery

Publisher: World Scientific

ISBN: 9814401242

Category: Computers

Page: 264

View: 4559

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Information Theory and Evolution discusses the phenomenon of life, including its origin and evolution (and also human cultural evolution), against the background of thermodynamics, statistical mechanics, and information theory. Among the central themes is the seeming contradiction between the second law of thermodynamics and the high degree of order and complexity produced by living systems. This paradox has its resolution in the information content of the Gibbs free energy that enters the biosphere from outside sources, as the author will show. The role of information in human cultural evolution is another focus of the book. The first edition of Information Theory and Evolution made a strong impact on thought in the field by bringing together results from many disciplines. The new second edition offers updated results based on reports of important new research in several areas, including exciting new studies of the human mitochondrial and Y-chromosomal DNA. Another extensive discussion featured in the second edition is contained in a new appendix devoted to the relationship of entropy and Gibbs free energy to economics. This appendix includes a review of the ideas of Alfred Lotka, Frederick Soddy, Nicholas Georgiescu-Roegen and Herman E. Daly, and discusses the relevance of these ideas to the current economic crisis. The new edition discusses current research on the origin of life, the distinction between thermodynamic information and cybernetic information, new DNA research and human prehistory, developments in current information technology, and the relationship between entropy and economics.

Information Theory

A Tutorial Introduction

Author: JV Stone

Publisher: Sebtel Press

ISBN: 0956372856

Category: Information theory

Page: 243

View: 9306

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Originally 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.

Entropy and Information Optics

Author: Francis T.S. Yu

Publisher: CRC Press

ISBN: 9780824703639

Category: Science

Page: 360

View: 3708

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"Identifies the relationship between entropy and information optics as the impetus for the research and development of high-speed, high-data-rate, and high-capacity communication systems. Examines computing, pattern recognition, and wavelet transformation."

Information Theory

Author: Robert B. Ash

Publisher: Courier Corporation

ISBN: 0486141454

Category: Technology & Engineering

Page: 352

View: 1527

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DIVAnalysis of channel models and proof of coding theorems; study of specific coding systems; and study of statistical properties of information sources. Sixty problems, with solutions. Advanced undergraduate to graduate level. /div

Information Theory for Continuous Systems

Author: Shunsuke Ihara

Publisher: World Scientific

ISBN: 9789810209858

Category: Computers

Page: 308

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This book provides a systematic mathematical analysis of entropy and stochastic processes, especially Gaussian processes, and its applications to information theory.The contents fall roughly into two parts. In the first part a unified treatment of entropy in information theory, probability theory and mathematical statistics is presented. The second part deals mostly with information theory for continuous communication systems. Particular emphasis is placed on the Gaussian channel.An advantage of this book is that, unlike most books on information theory, it places emphasis on continuous communication systems, rather than discrete ones.

Introduction to Coding and Information Theory

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 9780387947044

Category: Computers

Page: 323

View: 9716

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This book is an introduction to coding theory and information theory for undergraduate students of mathematics and computer science. Among the topics it discusses are: a review of probablity theory; the efficiency of codes, the capacity of communications channels, coding and decoding in the presence of errors, the general theory of linear codes, and examples of specific codes used in ordinalry communications as wwell as cryptography.

Information Theory and Statistics

Author: Solomon Kullback

Publisher: Courier Corporation

ISBN: 0486142043

Category: Mathematics

Page: 416

View: 6752

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Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.