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The Mathematical Theory Of Information

Author: Jan Kåhre
Publisher: Springer Science & Business Media
ISBN: 1461509750
Size: 51.52 MB
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The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.

Theory Of Information

Author: Mark Burgin
Publisher: World Scientific
ISBN: 9812835482
Size: 44.29 MB
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Presents a fresh approach to scientific understanding of information phenomena. Based on an analysis of information processes in nature, technology, and society, as well as on the main directions in information theory, this book offers a theory that synthesizes various directions into a unified system.

Information Coding And Mathematics

Author: Mario Blaum
Publisher: Springer Science & Business Media
ISBN: 1475735855
Size: 29.30 MB
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Information, Coding and Mathematics is a classic reference for both professional and academic researchers working in error-correction coding and decoding, Shannon theory, cryptography, digital communications, information security, and electronic engineering. The work represents a collection of contributions from leading experts in turbo coding, cryptography and sequences, Shannon theory and coding bounds, and decoding theory and applications. All of the contributors have individually and collectively dedicated their work as a tribute to the outstanding work of Robert J. McEliece. Information, Coding and Mathematics covers the latest advances in the widely used and rapidly developing field of information and communication technology.

Computer Aided Systems Theory Eurocast 2001

Author: Roberto Moreno-Diaz
Publisher: Springer
ISBN: 3540456546
Size: 47.31 MB
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The concept of CAST as Computer Aided Systems Theory, was introduced by F. Pichler in the late 1980s to include those computer theoretical and practical developments as tools to solve problems in System Science. It was considered as the third component (the other two being CAD and CAM) necessary to build the path from Computer and Systems Sciences to practical developments in Science and Engineering. The University of Linz organized the first CAST workshop in April 1988, which demonstrated the acceptance of the concepts by the scientific and technical community. Next, the University of Las Palmas de Gran Canaria joined the University of Linz to organize the first international meeting on CAST, (Las Palmas, February 1989), under the name EUROCAST’89. This was a very successful gathering of systems theorists, computer scientists, and engineers from most European countries, North America, and Japan. It was agreed that EUROCAST international conferences would be organized every two years, alternating between Las Palmas de Gran Canaria and a continental European location. Thus, successive EUROCAST meetings have taken place in Krems (1991), Las Palmas (1993), Innsbruck (1995), Las Palmas (1997), and Vienna (1999), in addition to an extra-European CAST Conference in Ottawa in 1994.

Applied And Computational Control Signals And Circuits

Author: Biswa Nath Datta
Publisher: Springer Science & Business Media
ISBN: 1461514711
Size: 61.35 MB
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Applied and Computational Control, Signals, and Circuits: Recent Developments is an interdisciplinary book blending mathematics, computational mathematics, scientific computing and software engineering with control and systems theory, signal processing, and circuit simulations. The material consists of seven state-of-the-art review chapters, each written by a leading expert in that field. Each of the technical chapters deals exclusively with some of the recent developments involving applications and computations of control, signals and circuits. Also included is a Chapter focusing on the newly developed Fortran-based software library, called SLICOT, for control systems design and analysis. This collection will be an excellent reference work for research scientists, practicing engineers, and graduate level students of control and systems, circuit design, power systems and signal processing.

Multimedia Signals And Systems

Author: Mrinal Kr Mandal
Publisher: Springer Science & Business Media
ISBN: 9781402072703
Size: 73.12 MB
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Multimedia Signals and Systems is an essential text for professional and academic researchers and students in the field of multimedia. Multimedia Signals and Systems is primarily a technical introductory level multimedia textbook, including problems, examples, and MATLAB® codes. It will be a stepping-stone for readers who want to research in audio processing, image and video processing, and data compression. This book will also be useful to readers who are carrying out research and development in systems areas such as television engineering and storage media. Anyone who seeks to learn the core multimedia signal processing techniques and systems will need Multimedia Signals and Systems. There are many chapters that are generic in nature and provide key concepts of multimedia systems to technical as well as non-technical persons. There are also several chapters that provide a mathematical/ analytical framework for basic multimedia signal processing. The readers are expected to have some prior knowledge about discrete signals and systems, such as Fourier transform and digital filters. However, a brief review of these theories is provided. Additional material for this book, including several MATLAB® codes along with a few test data samples; e.g., audio, image and video may be downloaded from http://extras.springer.com. Multimedia Signals and Systems is suitable for advanced-level courses in multimedia and is also a well-needed addition to the professional reference library in this area.

Communications And Cryptography

Author: Richard E. Blahut
Publisher: Springer Science & Business Media
ISBN: 1461526949
Size: 39.88 MB
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Information theory is an exceptional field in many ways. Technically, it is one of the rare fields in which mathematical results and insights have led directly to significant engineering payoffs. Professionally, it is a field that has sustained a remarkable degree of community, collegiality and high standards. James L. Massey, whose work in the field is honored here, embodies the highest standards of the profession in his own career. The book covers the latest work on: block coding, convolutional coding, cryptography, and information theory. The 44 contributions represent a cross-section of the world's leading scholars, scientists and researchers in information theory and communication. The book is rounded off with an index and a bibliography of publications by James Massey.

Finite Fields For Computer Scientists And Engineers

Author: Robert J. McEliece
Publisher: Springer Science & Business Media
ISBN: 1461319838
Size: 42.43 MB
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This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.

Effective Polynomial Computation

Author: Richard Zippel
Publisher: Springer Science & Business Media
ISBN: 1461531888
Size: 16.51 MB
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Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

Applications Of Finite Fields

Author: Alfred J. Menezes
Publisher: Springer Science & Business Media
ISBN: 1475722265
Size: 50.37 MB
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The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.