Abstract Methods In Information Theory

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Abstract Methods in Information Theory

Author : Yichir Kakihara
Publisher : World Scientific
ISBN 13 : 9789810237110
Total Pages : 272 pages
Book Rating : 4.2/5 (371 download)

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Book Synopsis Abstract Methods in Information Theory by : Yichir Kakihara

Download or read book Abstract Methods in Information Theory written by Yichir Kakihara and published by World Scientific. This book was released on 1999 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Methods In Information Theory (Second Edition)

Author : Yuichiro Kakihara
Publisher : World Scientific
ISBN 13 : 9814759252
Total Pages : 413 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Abstract Methods In Information Theory (Second Edition) by : Yuichiro Kakihara

Download or read book Abstract Methods In Information Theory (Second Edition) written by Yuichiro Kakihara and published by World Scientific. This book was released on 2016-06-09 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information Theory is studied from the following points of view: (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 functional analysis and operator theory as well as probability theory. Ergodic, mixing, and AMS channels are also considered in detail with some illustrations. In this second edition, channel operators are studied in many aspects, which generalize ordinary channels. Also Gaussian channels are considered in detail together with Gaussian measures on a Hilbert space. The Special Topics chapter deals with features such as generalized capacity, channels with an intermediate noncommutative system, and von Neumann algebra method for channels. Finally, quantum (noncommutative) information channels are examined in an independent chapter, which may be regarded as an introduction to quantum information theory. Von Neumann entropy is introduced and its generalization to a C*-algebra setting is given. Basic results on quantum channels and entropy transmission are also considered.

Information-Spectrum Methods in Information Theory

Author : Te Sun Han
Publisher : Springer Science & Business Media
ISBN 13 : 3662120666
Total Pages : 552 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Information-Spectrum Methods in Information Theory by : Te Sun Han

Download or read book Information-Spectrum Methods in Information Theory written by Te Sun Han and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book nicely complements the existing literature on information and coding theory by concentrating on arbitrary nonstationary and/or nonergodic sources and channels with arbitrarily large alphabets. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems." -- MATHEMATICAL REVIEWS

Information Theory and Network Coding

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
ISBN 13 : 0387792341
Total Pages : 592 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Information Theory and Network Coding by : Raymond W. Yeung

Download or read book Information Theory and Network Coding written by Raymond W. Yeung and published by Springer Science & Business Media. This book was released on 2008-08-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and the Central Limit Theorem

Author : Oliver Thomas Johnson
Publisher : World Scientific
ISBN 13 : 1860944736
Total Pages : 224 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Information Theory and the Central Limit Theorem by : Oliver Thomas Johnson

Download or read book Information Theory and the Central Limit Theorem written by Oliver Thomas Johnson and published by World Scientific. This book was released on 2004 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems.

Coding and Information Theory

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387978123
Total Pages : 520 pages
Book Rating : 4.9/5 (781 download)

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Book Synopsis Coding and Information Theory by : Steven Roman

Download or read book Coding and Information Theory written by Steven Roman and published by Springer Science & Business Media. This book was released on 1992-06-04 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.

Information Theory

Author : Defense Documentation Center (U.S.)
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Information Theory by : Defense Documentation Center (U.S.)

Download or read book Information Theory written by Defense Documentation Center (U.S.) and published by . This book was released on 1962 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A First Course in Information Theory

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
ISBN 13 : 1441986081
Total Pages : 426 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A First Course in Information Theory by : Raymond W. Yeung

Download or read book A First Course in Information Theory written by Raymond W. Yeung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

Algorithmic Information Theory for Physicists and Natural Scientists

Author : Sean D Devine
Publisher :
ISBN 13 : 9780750326414
Total Pages : 238 pages
Book Rating : 4.3/5 (264 download)

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Book Synopsis Algorithmic Information Theory for Physicists and Natural Scientists by : Sean D Devine

Download or read book Algorithmic Information Theory for Physicists and Natural Scientists written by Sean D Devine and published by . This book was released on 2020-06-11 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however, some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to scientists. This book has been written in the hope that readers will be able to absorb the key ideas behind AIT so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest. The theoretical underpinning of AIT is outlined in the earlier chapters, while later chapters focus on the applications, drawing attention to the thermodynamic commonality between ordered physical systems such as the alignment of magnetic spins, the maintenance of a laser distant from equilibrium, and ordered living systems such as bacterial systems, an ecology, and an economy. Key Features Presents a mathematically complex subject in language accessible to scientists Provides rich insights into modelling far-from-equilibrium systems Emphasises applications across range of fields, including physics, biology and econophysics Empowers scientists to apply these mathematical tools to their own research

The Functional Analysis of Quantum Information Theory

Author : Ved Prakash Gupta
Publisher : Springer
ISBN 13 : 3319167189
Total Pages : 149 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Functional Analysis of Quantum Information Theory by : Ved Prakash Gupta

Download or read book The Functional Analysis of Quantum Information Theory written by Ved Prakash Gupta and published by Springer. This book was released on 2015-05-28 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. Starting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. On the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting.

Introduction to Information Theory and Data Compression, Second Edition

Author : D.C. Hankerson
Publisher : CRC Press
ISBN 13 : 9781584883135
Total Pages : 394 pages
Book Rating : 4.8/5 (831 download)

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Book Synopsis Introduction to Information Theory and Data Compression, Second Edition by : D.C. Hankerson

Download or read book Introduction to Information Theory and Data Compression, Second Edition written by D.C. Hankerson and published by CRC Press. This book was released on 2003-02-26 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed so that the data compression section requires no prior knowledge of information theory. The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory, the authors then apply the theory to memoryless, discrete channels with zeroth-order, one-state sources. The chapters on data compression acquaint students with a myriad of lossless compression methods and then introduce two lossy compression methods. Students emerge from this study competent in a wide range of techniques. The authors' presentation is highly practical but includes some important proofs, either in the text or in the exercises, so instructors can, if they choose, place more emphasis on the mathematics. Introduction to Information Theory and Data Compression, Second Edition is ideally suited for an upper-level or graduate course for students in mathematics, engineering, and computer science. Features: Expanded discussion of the historical and theoretical basis of information theory that builds a firm, intuitive grasp of the subject Reorganization of theoretical results along with new exercises, ranging from the routine to the more difficult, that reinforce students' ability to apply the definitions and results in specific situations. Simplified treatment of the algorithm(s) of Gallager and Knuth Discussion of the information rate of a code and the trade-off between error correction and information rate Treatment of probabilistic finite state source automata, including basic results, examples, references, and exercises Octave and MATLAB image compression codes included in an appendix for use with the exercises and projects involving transform methods Supplementary materials, including software, available for download from the authors' Web site at www.dms.auburn.edu/compression

Information, Physics, and Computation

Author : Marc Mézard
Publisher : Oxford University Press
ISBN 13 : 019857083X
Total Pages : 584 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Information, Physics, and Computation by : Marc Mézard

Download or read book Information, Physics, and Computation written by Marc Mézard and published by Oxford University Press. This book was released on 2009-01-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Information Theory

Author : Sergio Verdú
Publisher : Wiley-IEEE Press
ISBN 13 :
Total Pages : 776 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Information Theory by : Sergio Verdú

Download or read book Information Theory written by Sergio Verdú and published by Wiley-IEEE Press. This book was released on 2000 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: See:

Information Theory

Author : JV Stone
Publisher : Sebtel Press
ISBN 13 : 0956372856
Total Pages : 243 pages
Book Rating : 4.9/5 (563 download)

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Book Synopsis Information Theory by : JV Stone

Download or read book Information Theory written by JV Stone and published by Sebtel Press. This book was released on 2015-01-01 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematical Theory of Communication

Author : Claude E Shannon
Publisher : University of Illinois Press
ISBN 13 : 025209803X
Total Pages : 141 pages
Book Rating : 4.2/5 (52 download)

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Book Synopsis The Mathematical Theory of Communication by : Claude E Shannon

Download or read book The Mathematical Theory of Communication written by Claude E Shannon and published by University of Illinois Press. This book was released on 1998-09-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

An Introduction to Single-User Information Theory

Author : Fady Alajaji
Publisher : Springer
ISBN 13 : 9811080011
Total Pages : 333 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis An Introduction to Single-User Information Theory by : Fady Alajaji

Download or read book An Introduction to Single-User Information Theory written by Fady Alajaji and published by Springer. This book was released on 2018-04-24 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Information Theory

Author : Thomas M. Cover
Publisher : John Wiley & Sons
ISBN 13 : 1118585771
Total Pages : 788 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Elements of Information Theory by : Thomas M. Cover

Download or read book Elements of Information Theory written by Thomas M. Cover and published by John Wiley & Sons. This book was released on 2012-11-28 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.