Abstract Methods In Information Theory Second Edition

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Abstract Methods In Information Theory (Second Edition)

Author : Yuichiro Kakihara
Publisher : World Scientific
ISBN 13 : 9814759252
Total Pages : 413 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Abstract Methods In Information Theory (Second Edition) by : Yuichiro Kakihara

Download or read book Abstract Methods In Information Theory (Second Edition) written by Yuichiro Kakihara and published by World Scientific. This book was released on 2016-06-09 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Methods in Information Theory

Author : Yichir Kakihara
Publisher : World Scientific
ISBN 13 : 9789810237110
Total Pages : 272 pages
Book Rating : 4.2/5 (371 download)

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Book Synopsis Abstract Methods in Information Theory by : Yichir Kakihara

Download or read book Abstract Methods in Information Theory written by Yichir Kakihara and published by World Scientific. This book was released on 1999 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Processes: Harmonizable Theory

Author : Malempati Madhusudana Rao
Publisher : World Scientific
ISBN 13 : 9811213674
Total Pages : 341 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Stochastic Processes: Harmonizable Theory by : Malempati Madhusudana Rao

Download or read book Stochastic Processes: Harmonizable Theory written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2020-09-21 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.

Hilbert And Banach Space-valued Stochastic Processes

Author : Yuichiro Kakihara
Publisher : World Scientific
ISBN 13 : 9811211760
Total Pages : 539 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Hilbert And Banach Space-valued Stochastic Processes by : Yuichiro Kakihara

Download or read book Hilbert And Banach Space-valued Stochastic Processes written by Yuichiro Kakihara and published by World Scientific. This book was released on 2021-07-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.

Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences

Author : Rupert Lasser
Publisher : World Scientific
ISBN 13 : 9811266212
Total Pages : 621 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences by : Rupert Lasser

Download or read book Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences written by Rupert Lasser and published by World Scientific. This book was released on 2022-12-06 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.

Linear Models And Regression With R: An Integrated Approach

Author : Debasis Sengupta
Publisher : World Scientific
ISBN 13 : 9811200424
Total Pages : 773 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Linear Models And Regression With R: An Integrated Approach by : Debasis Sengupta

Download or read book Linear Models And Regression With R: An Integrated Approach written by Debasis Sengupta and published by World Scientific. This book was released on 2019-07-30 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features:

Elements of Information Theory

Author : Thomas M. Cover
Publisher : John Wiley & Sons
ISBN 13 : 1118585771
Total Pages : 788 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Elements of Information Theory by : Thomas M. Cover

Download or read book Elements of Information Theory written by Thomas M. Cover and published by John Wiley & Sons. This book was released on 2012-11-28 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Information Theory and Data Compression, Second Edition

Author : D.C. Hankerson
Publisher : CRC Press
ISBN 13 : 9781584883135
Total Pages : 394 pages
Book Rating : 4.8/5 (831 download)

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Book Synopsis Introduction to Information Theory and Data Compression, Second Edition by : D.C. Hankerson

Download or read book Introduction to Information Theory and Data Compression, Second Edition written by D.C. Hankerson and published by CRC Press. This book was released on 2003-02-26 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 prior knowledge of information theory. The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory, the authors then apply the theory to memoryless, discrete channels with zeroth-order, one-state sources. The chapters on data compression acquaint students with a myriad of lossless compression methods and then introduce two lossy compression methods. Students emerge from this study competent in a wide range of techniques. The authors' presentation is highly practical but includes some important proofs, either in the text or in the exercises, so instructors can, if they choose, place more emphasis on the mathematics. Introduction to Information Theory and Data Compression, Second Edition is ideally suited for an upper-level or graduate course for students in mathematics, engineering, and computer science. Features: Expanded discussion of the historical and theoretical basis of information theory that builds a firm, intuitive grasp of the subject Reorganization of theoretical results along with new exercises, ranging from the routine to the more difficult, that reinforce students' ability to apply the definitions and results in specific situations. Simplified treatment of the algorithm(s) of Gallager and Knuth Discussion of the information rate of a code and the trade-off between error correction and information rate Treatment of probabilistic finite state source automata, including basic results, examples, references, and exercises Octave and MATLAB image compression codes included in an appendix for use with the exercises and projects involving transform methods Supplementary materials, including software, available for download from the authors' Web site at www.dms.auburn.edu/compression

Coding and Information Theory

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387978123
Total Pages : 520 pages
Book Rating : 4.9/5 (781 download)

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Book Synopsis Coding and Information Theory by : Steven Roman

Download or read book Coding and Information Theory written by Steven Roman and published by Springer Science & Business Media. This book was released on 1992-06-04 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cryptography, Information Theory, and Error-Correction

Author : Aiden A. Bruen
Publisher : John Wiley & Sons
ISBN 13 : 1119582407
Total Pages : 688 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Cryptography, Information Theory, and Error-Correction by : Aiden A. Bruen

Download or read book Cryptography, Information Theory, and Error-Correction written by Aiden A. Bruen and published by John Wiley & Sons. This book was released on 2021-10-08 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: CRYPTOGRAPHY, INFORMATION THEORY, AND ERROR-CORRECTION A rich examination of the technologies supporting secure digital information transfers from respected leaders in the field As technology continues to evolve Cryptography, Information Theory, and Error-Correction: A Handbook for the 21ST Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book. This book is geared toward a broad audience. It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. It is also an authoritative overview for professionals working at financial institutions, law firms, and governments who need up-to-date information to make critical decisions. The book’s discussions will be of interest to those involved in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars. With its reader-friendly style and interdisciplinary emphasis this book serves as both an ideal teaching text and a tool for self-learning for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs. Six new chapters cover current topics like Internet of Things security, new identities in information theory, blockchains, cryptocurrency, compression, cloud computing and storage. Increased security and applicable research in elliptic curve cryptography are also featured. The book also: Shares vital, new research in the field of information theory Provides quantum cryptography updates Includes over 350 worked examples and problems for greater understanding of ideas. Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.

Structural Aspects in the Theory of Probability

Author : Herbert Heyer
Publisher : World Scientific
ISBN 13 : 9814282480
Total Pages : 425 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Structural Aspects in the Theory of Probability by : Herbert Heyer

Download or read book Structural Aspects in the Theory of Probability written by Herbert Heyer and published by World Scientific. This book was released on 2010 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

Random and Vector Measures

Author : M. M. Rao
Publisher : World Scientific
ISBN 13 : 9814350826
Total Pages : 553 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Random and Vector Measures by : M. M. Rao

Download or read book Random and Vector Measures written by M. M. Rao and published by World Scientific. This book was released on 2011 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up.

Information Theory and Network Coding

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
ISBN 13 : 0387792341
Total Pages : 592 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Information Theory and Network Coding by : Raymond W. Yeung

Download or read book Information Theory and Network Coding written by Raymond W. Yeung and published by Springer Science & Business Media. This book was released on 2008-08-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Coding and Information Theory

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387947044
Total Pages : 344 pages
Book Rating : 4.9/5 (47 download)

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Book Synopsis Introduction to Coding and Information Theory by : Steven Roman

Download or read book Introduction to Coding and Information Theory written by Steven Roman and published by Springer Science & Business Media. This book was released on 1996-11-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.

A First Course in Information Theory

Author : Raymond W. Yeung
Publisher : Springer Science & Business Media
ISBN 13 : 1441986081
Total Pages : 426 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A First Course in Information Theory by : Raymond W. Yeung

Download or read book A First Course in Information Theory written by Raymond W. Yeung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Graph Theory, Second Edition

Author : Jonathan L. Gross
Publisher : CRC Press
ISBN 13 : 1439880182
Total Pages : 1634 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Handbook of Graph Theory, Second Edition by : Jonathan L. Gross

Download or read book Handbook of Graph Theory, Second Edition written by Jonathan L. Gross and published by CRC Press. This book was released on 2013-12-17 with total page 1634 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Coding and Information Theory

Author : Richard Wesley Hamming
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Coding and Information Theory by : Richard Wesley Hamming

Download or read book Coding and Information Theory written by Richard Wesley Hamming and published by Prentice Hall. This book was released on 1986 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).