Entropy And Information Theory
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Entropy And Information Theory
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Author : Robert M. Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Entropy And Information Theory written by Robert M. Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
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.
Mathematical Foundations Of Information Theory
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Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1957-01-01
Mathematical Foundations Of Information Theory written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957-01-01 with Mathematics categories.
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.
An Introduction To Transfer Entropy
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Author : Terry Bossomaier
language : en
Publisher: Springer
Release Date : 2016-11-15
An Introduction To Transfer Entropy written by Terry Bossomaier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-15 with Computers categories.
This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance. The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.
Elements Of Information Theory
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Author : Thomas M. Cover
language : en
Publisher: John Wiley & Sons
Release Date : 2012-11-28
Elements Of Information Theory written by Thomas M. Cover and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-28 with Computers categories.
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.
New Foundations For Information Theory
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Author : David Ellerman
language : en
Publisher: Springer Nature
Release Date : 2021-10-30
New Foundations For Information Theory written by David Ellerman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-30 with Philosophy categories.
This 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.
A First Course In Information Theory
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Author : Raymond W. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Information Theory written by Raymond W. Yeung and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
Information Theory And The Central Limit Theorem
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Author : Oliver Johnson
language : en
Publisher: World Scientific
Release Date : 2004
Information Theory And The Central Limit Theorem written by Oliver Johnson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Annotation. - Presents surprising, interesting connections between two apparently separate areas of mathematics- Written by one of the researchers who discovered these connections- Offers a new way of looking at familiar results.
Elements Of Information Theory
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Author : T. M. Cover
language : en
Publisher: John Wiley & Sons
Release Date : 1999
Elements Of Information Theory written by T. M. Cover and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Information theory categories.
· Entropy, Relative Entropy and Mutual Information· The Asymptotic Equipartition Property· Entropy Rates of a Stochastic Process· Data Compression· Gambling and Data Compression· Kolmogorov Complexity· Channel Capacity· Differential Entropy· The Gaussian Channel· Maximum Entropy and Spectral Estimation· Information Theory and Statistics· Rate Distortion Theory· Network Information Theory· Information Theory and the Stock Market· Inequalities in Information Theory
Optics And Information Theory
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Author : Francis T. S. Yu
language : en
Publisher: John Wiley & Sons
Release Date : 1976
Optics And Information Theory written by Francis T. S. Yu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Computers categories.
An Introduction To Single User Information Theory
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Author : Fady Alajaji
language : en
Publisher: Springer
Release Date : 2018-04-24
An Introduction To Single User Information Theory written by Fady Alajaji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-24 with Mathematics categories.
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.