Abstract Methods In Information Theory
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| Author | : Yichir Kakihara |
| Publisher | : World Scientific |
| Total Pages | : 272 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9789810237110 |
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.
| Author | : Yuichiro Kakihara |
| Publisher | : World Scientific |
| Total Pages | : 413 |
| Release | : 2016-06-09 |
| Genre | : Computers |
| ISBN | : 9814759252 |
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.
| Author | : Raymond W. Yeung |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 592 |
| Release | : 2008-08-28 |
| Genre | : Computers |
| ISBN | : 0387792341 |
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.
| Author | : David J. C. MacKay |
| Publisher | : Cambridge University Press |
| Total Pages | : 694 |
| Release | : 2003-09-25 |
| Genre | : Computers |
| ISBN | : 9780521642989 |
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.
| Author | : Robert B. Ash |
| Publisher | : Halsted Press |
| Total Pages | : 360 |
| Release | : 1965 |
| Genre | : Computers |
| ISBN | : |
| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 520 |
| Release | : 1992-06-04 |
| Genre | : Mathematics |
| ISBN | : 9780387978123 |
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.
| Author | : Defense Documentation Center (U.S.) |
| Publisher | : |
| Total Pages | : 1032 |
| Release | : 1963 |
| Genre | : Science |
| ISBN | : |
| Author | : Richard Wesley Hamming |
| Publisher | : Prentice Hall |
| Total Pages | : 280 |
| Release | : 1986 |
| Genre | : Computers |
| ISBN | : |
Focusing on both theory and practical applications, this volume combines in a natural way the two major aspects of information representation--representation for storage (coding theory) and representation for transmission (information theory).
| Author | : Defense Documentation Center (U.S.) |
| Publisher | : |
| Total Pages | : 72 |
| Release | : 1962 |
| Genre | : Information theory |
| ISBN | : |
| Author | : Sean D Devine |
| Publisher | : |
| Total Pages | : 238 |
| Release | : 2020-06-11 |
| Genre | : |
| ISBN | : 9780750326414 |
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
