Abstract Methods In Information Theory

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Abstract Methods In Information Theory

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Author : Yuichiro Kakihara
language : en
Publisher: World Scientific
Release Date : 1999-10-15

Abstract Methods In Information Theory written by Yuichiro Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-15 with Mathematics categories.

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.

Abstract Methods In Information Theory Second Edition

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Author : Yuichiro Kakihara
language : en
Publisher: World Scientific
Release Date : 2016-06-09

Abstract Methods In Information Theory Second Edition written by Yuichiro Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-09 with Computers categories.

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.

Information Theory And Network Coding

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Author : Raymond W. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-28

Information Theory And Network Coding 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 2008-08-28 with Computers categories.

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.

Modern Cryptography Volume 1

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Author : Zhiyong Zheng
language : en
Publisher: Springer Nature
Release Date : 2022-04-16

Modern Cryptography Volume 1 written by Zhiyong Zheng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-16 with Business & Economics categories.

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas.

Proceedings Of The Fourth Berkeley Symposium On Mathematical Statistics And Probability

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Author : Jerzy Neyman
language : en
Publisher: Univ of California Press
Release Date : 1960

Proceedings Of The Fourth Berkeley Symposium On Mathematical Statistics And Probability written by Jerzy Neyman and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematical statistics categories.

Technical Abstract Bulletin

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Author :
language : en
Publisher:
Release Date :

Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.

Rule Based Systems For Big Data

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Author : Han Liu
language : en
Publisher: Springer
Release Date : 2015-09-09

Rule Based Systems For Big Data written by Han Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Technology & Engineering categories.

The ideas introduced in this book explore the relationships among rule based systems, machine learning and big data. Rule based systems are seen as a special type of expert systems, which can be built by using expert knowledge or learning from real data. The book focuses on the development and evaluation of rule based systems in terms of accuracy, efficiency and interpretability. In particular, a unified framework for building rule based systems, which consists of the operations of rule generation, rule simplification and rule representation, is presented. Each of these operations is detailed using specific methods or techniques. In addition, this book also presents some ensemble learning frameworks for building ensemble rule based systems.

Introduction To Information Theory And Data Compression

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Author : Peter D. Johnson Jr.
language : en
Publisher: CRC Press
Release Date : 2003-02-26

Introduction To Information Theory And Data Compression written by Peter D. Johnson Jr. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-26 with Computers categories.

An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed so that the data compression section requires no pr

Information Theory

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Author :
language : en
Publisher: Pergamon
Release Date : 1989

Information Theory written by and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.

Proceedings of the International Workshop on Information Theory held in Beijing, July, 1988. Topics include: coding; networks and protocols; channels and sequences; decoding, detection, and estimation; and source and channel coding. The printing, from photocopies of contributor's papers, is inconsis

Abstract Methods In Information Theory

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Author : Yūichirō Kakihara
language : en
Publisher:
Release Date : 2016

Abstract Methods In Information Theory written by Yūichirō Kakihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Functional analysis categories.

"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."--