Entropy and Information Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Entropy and Information Theory write by Robert M. Gray. This book was released on 2013-03-14. Entropy and Information Theory available in PDF, EPUB and Kindle. 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.
New Foundations for Information Theory
New Foundations for Information Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Foundations for Information Theory write by David Ellerman. This book was released on 2021-10-30. New Foundations for Information Theory available in PDF, EPUB and Kindle. 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.
An Introduction to Transfer Entropy
An Introduction to Transfer Entropy - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Transfer Entropy write by Terry Bossomaier. This book was released on 2016-11-15. An Introduction to Transfer Entropy available in PDF, EPUB and Kindle. 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.
Entropy and Information Theory
Entropy and Information Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Entropy and Information Theory write by Robert M. Gray. This book was released on 2011-02-03. Entropy and Information Theory available in PDF, EPUB and Kindle. 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.
Entropy and Information
Entropy and Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Entropy and Information write by Mikhail V. Volkenstein. This book was released on 2009-10-27. Entropy and Information available in PDF, EPUB and Kindle. 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.
