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Information Theory for Continuous Systems

Information Theory for Continuous Systems
Author: Shunsuke Ihara
Publisher: World Scientific
Total Pages: 332
Release: 1993
Genre: Computers
ISBN: 9789810209858
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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.

Information Theory

Information Theory
Author: Stanford Goldman
Publisher: Dover Publications
Total Pages: 414
Release: 1953
Genre: Computers
ISBN:
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Students of electrical engineering or applied mathematics can find no clearer presentation of the principles of information theory than this excellent introduction. After explaining the nature of information theory and its problems, the author examines a variety of important topics: information theory of discrete systems; properties of continuous signals; ergodic ensembles and random noise; entropy of continuous distributions; the transmission of information in band-limited systems having a continuous range of values; an introduction to the use of signal space; information theory aspects of modulation and noise reduction; and linear correlation, filtering, and prediction. Numerous problems appear throughout the text, many with complete solutions. 1953 ed.

Entropy and Information Theory

Entropy and Information Theory
Author: Robert M. Gray
Publisher: Springer Science & Business Media
Total Pages: 346
Release: 2013-03-14
Genre: Computers
ISBN: 1475739826
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This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.

The Mathematical Theory of Communication

The Mathematical Theory of Communication
Author: Claude E Shannon
Publisher: University of Illinois Press
Total Pages: 141
Release: 1998-09-01
Genre: Language Arts & Disciplines
ISBN: 025209803X
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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.

The Mathematical Theory of Information

The Mathematical Theory of Information
Author: Jan Kåhre
Publisher: Springer Science & Business Media
Total Pages: 528
Release: 2002-06-30
Genre: Technology & Engineering
ISBN: 9781402070648
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The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.

Elements of Information Theory

Elements of Information Theory
Author: Thomas M. Cover
Publisher: John Wiley & Sons
Total Pages: 788
Release: 2012-11-28
Genre: Computers
ISBN: 1118585771
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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.

Information Theory for Systems Engineers

Information Theory for Systems Engineers
Author: L.P. Hyvärinen
Publisher: Springer Science & Business Media
Total Pages: 216
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642870929
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This book is based on lectures given by the author at the IBM European Systems Research Institute (ESRI) in Geneva. Information Theory on the syntactic level, as introduced by Claude Shannon in 1949, has many limitations when applied to information processing by computers. But in spite of some obvious shortcomings, the underlyin~ principles are of fundamental importance for systems engineers in understanding the nature of the problems of handling information, its acquisition, storage, processing, and interpretation. The lectures, as presented in this book, attempt to give an exposition of the lovical foundation and basic principles, and to provide at the same time a basis for further study in more specific areas of this expan1in~ theory, such as coding, detection, pattern recognition, and filtering. Most of the problems in Appendix C are intended as extensions of the text, while calling for actjve participation by the stu1ent. Some other problems are direct applications of the theory to specific situations. Some problems require extensive numerical calculations. It is assumed in those cases that the student has access to a computer and that he is capable of writing the necessary programs. The stu1ent is assumed to have a good command of the calculus, and of the theory of probability as well as statistics. Therefore no basic mathematical concepts are discussed in this IV book. The Fourier transform and some related mathematical concepts are introduced in Appendix A.

Relative Information

Relative Information
Author: Guy Jumarie
Publisher: Springer Science & Business Media
Total Pages: 279
Release: 2012-12-06
Genre: Science
ISBN: 3642840175
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For four decades, information theory has been viewed almost exclusively as a theory based upon the Shannon measure of uncertainty and information, usually referred to as Shannon entropy. Since the publication of Shannon's seminal paper in 1948, the theory has grown extremely rapidly and has been applied with varied success in almost all areas of human endeavor. At this time, the Shannon information theory is a well established and developed body of knowledge. Among its most significant recent contributions have been the use of the complementary principles of minimum and maximum entropy in dealing with a variety of fundamental systems problems such as predic tive systems modelling, pattern recognition, image reconstruction, and the like. Since its inception in 1948, the Shannon theory has been viewed as a restricted information theory. It has often been argued that the theory is capable of dealing only with syntactic aspects of information, but not with its semantic and pragmatic aspects. This restriction was considered a v~rtue by some experts and a vice by others. More recently, however, various arguments have been made that the theory can be appropriately modified to account for semantic aspects of in formation as well. Some of the most convincing arguments in this regard are in cluded in Fred Dretske's Know/edge & Flow of Information (The M.LT. Press, Cambridge, Mass., 1981) and in this book by Guy lumarie.

Information Theory and Network Coding

Information Theory and Network Coding
Author: Raymond W. Yeung
Publisher: Springer Science & Business Media
Total Pages: 592
Release: 2008-09-10
Genre: Computers
ISBN: 0387792333
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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, Inference and Learning Algorithms

Information Theory, Inference and Learning Algorithms
Author: David J. C. MacKay
Publisher: Cambridge University Press
Total Pages: 694
Release: 2003-09-25
Genre: Computers
ISBN: 9780521642989
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Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.