The Mathematical Theory Of Information

Author : Jan Kåhre
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 44,5 Mb
Release : 2002-06-30
Category : Technology & Engineering
ISBN : 1402070640

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The Mathematical Theory of Information by Jan Kåhre Pdf

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.

Author : Claude E Shannon,Warren Weaver
Publisher : University of Illinois Press
Page : 144 pages
File Size : 52,5 Mb
Release : 1998-09-01
Category : Language Arts & Disciplines
ISBN : 9780252098031

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The Mathematical Theory of Communication by Claude E Shannon,Warren Weaver Pdf

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.

Author : Claude Elwood Shannon,Warren Weaver
Publisher : Unknown
Page : 136 pages
File Size : 53,6 Mb
Release : 1962
Category : Information theory
ISBN : STANFORD:36105024124401

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The Mathematical Theory of Communication by Claude Elwood Shannon,Warren Weaver Pdf

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 130 pages
File Size : 55,6 Mb
Release : 1957-01-01
Category : Mathematics
ISBN : 9780486604343

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Mathematical Foundations of Information Theory by Aleksandr I?Akovlevich Khinchin Pdf

First 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 : Luciano Floridi
Publisher : Oxford University Press
Page : 153 pages
File Size : 43,6 Mb
Release : 2010-02-25
Category : Computers
ISBN : 9780199551378

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Information: A Very Short Introduction by Luciano Floridi Pdf

Introduction; 1 The information revolution; 2 The language of information; 3 Mathematical information; 4 Semantic information; 5 Physical information; 6 Biological information; 7 Economic information; 8 The ethics of information; Conclusion; References.

Author : Nathaniel F. G. Martin,James W. England
Publisher : Cambridge University Press
Page : 292 pages
File Size : 53,6 Mb
Release : 2011-06-02
Category : Computers
ISBN : 0521177383

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Mathematical Theory of Entropy by Nathaniel F. G. Martin,James W. England Pdf

This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.

Author : Da-Quan Jiang,Donghua Jiang
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 51,8 Mb
Release : 2004
Category : Markov processes
ISBN : 3540206116

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Mathematical Theory of Nonequilibrium Steady States by Da-Quan Jiang,Donghua Jiang Pdf

Author : Jan Kahre
Publisher : Unknown
Page : 520 pages
File Size : 47,8 Mb
Release : 2002-06-30
Category : Electronic
ISBN : 1461509769

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The Mathematical Theory of Information by Jan Kahre Pdf

The Mathematical Theory of Information presents a new mathematical theory of information, built on a single powerful postulate: the Law of Diminishing Information. The concept of information is here, for the first time, defined mathematically by adding this postulate to the axioms of the probability theory. The Law of Diminishing Information is founded on a fusion of two fundamental ideas: Carnap and Bar-Hillel's Ideal Receiver' and Shannon's Noisy Channel'. The Law of Diminishing Information is applied to information technology, game theory, legislation, logic of research, algorithmic information, chaos theory, control engineering, medical tests, and biological evolution. In physics, both the Second Law of Thermodynamics and Schrodinger's wave function are derived from the Law of Diminishing Information. Conventional information theory, that of telecommunications, is analyzed as a special case, and eight conditions for its applicability are listed. The reader will get the essential ideas to understand and use the concept of information. The Mathematical Theory of Information is suitable as a textbook in general information theory for students of technical, scientific, and mathematical subjects. The book is ideal as a supplementary textbook in traditional courses on telecommunications information theory at all levels. The website of the book is www.matheory.info.

Author : John Watrous
Publisher : Unknown
Page : 599 pages
File Size : 44,9 Mb
Release : 2018-04-26
Category : Computers
ISBN : 9781107180567

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The Theory of Quantum Information by John Watrous Pdf

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

Author : Fady Alajaji,Po-Ning Chen
Publisher : Springer
Page : 323 pages
File Size : 44,7 Mb
Release : 2018-04-24
Category : Mathematics
ISBN : 9789811080012

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An Introduction to Single-User Information Theory by Fady Alajaji,Po-Ning Chen Pdf

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.

Author : JV Stone
Publisher : Sebtel Press
Page : 243 pages
File Size : 43,5 Mb
Release : 2015-01-01
Category : Business & Economics
ISBN : 9780956372857

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Information Theory by JV Stone Pdf

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.

Author : A. Ya. Khinchin
Publisher : Courier Corporation
Page : 130 pages
File Size : 55,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486318448

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Mathematical Foundations of Information Theory by A. Ya. Khinchin Pdf

First 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 : Robert B. Ash
Publisher : Halsted Press
Page : 360 pages
File Size : 47,5 Mb
Release : 1965
Category : Computers
ISBN : UOM:39015001313777

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Information Theory by Robert B. Ash Pdf

Author : Christoph Arndt
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642566691

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Information Measures by Christoph Arndt Pdf

From the reviews: "Bioinformaticians are facing the challenge of how to handle immense amounts of raw data, [...] and render them accessible to scientists working on a wide variety of problems. [This book] can be such a tool." IEEE Engineering in Medicine and Biology

Author : Robert M. Gray
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 40,7 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475739824

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Entropy and Information Theory by Robert M. Gray Pdf

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.