Codes, Curves, and Signals

Codes, Curves, and Signals PDF

Author: Alexander Vardy

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 265

ISBN-13: 1461551218

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Codes, Curves, and Signals: Common Threads in Communications is a collection of seventeen contributions from leading researchers in communications. The book provides a representative cross-section of cutting edge contemporary research in the fields of algebraic curves and the associated decoding algorithms, the use of signal processing techniques in coding theory, and the application of information-theoretic methods in communications and signal processing. The book is organized into three parts: Curves and Codes, Codes and Signals, and Signals and Information. Codes, Curves, and Signals: Common Threads in Communications is a tribute to the broad and profound influence of Richard E. Blahut on the fields of algebraic coding, information theory, and digital signal processing. All the contributors have individually and collectively dedicated their work to R. E. Blahut. Codes, Curves, and Signals: Common Threads in Communications is an excellent reference for researchers and professionals.

Algebraic Codes on Lines, Planes, and Curves

Algebraic Codes on Lines, Planes, and Curves PDF

Author: Richard E. Blahut

Publisher: Cambridge University Press

Published: 2008-04-03

Total Pages: 10

ISBN-13: 1139469460

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The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.

Codes, Cryptology and Curves with Computer Algebra

Codes, Cryptology and Curves with Computer Algebra PDF

Author: Ruud Pellikaan

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 612

ISBN-13: 1108547826

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This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

Signal Coding and Processing

Signal Coding and Processing PDF

Author: Graham Wade

Publisher: Cambridge University Press

Published: 1994-09-08

Total Pages: 464

ISBN-13: 9780521423366

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This comprehensive text is a revised and greatly expanded second edition of a book first published in 1987, and provides a thorough introduction to the complex fields of signal coding and signal processing. Among the key topics covered are: the fundamentals of pulse code modulation; modern data compression techniques; block and convolutional error control codes; transmission coding techniques; digital filters; infinite and finite impulse response filters; adaptive filters; and fast Fourier transform theory, implementation and applications. Complete with problems and solutions, and containing over 230 diagrams, this textbook will be invaluable to third and fourth year undergraduates in electronic, electrical or communication engineering. It will also act as a useful reference for anyone working in this technologically important field.

Codes and Curves

Codes and Curves PDF

Author: Judy L. Walker

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 66

ISBN-13: 9781470418236

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When information is transmitted, errors are likely to occur. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes, one can see how to define new codes based on divisors on algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously known codes. This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above is discussed.

Algebraic Codes for Data Transmission

Algebraic Codes for Data Transmission PDF

Author: Richard E. Blahut

Publisher: Cambridge University Press

Published: 2003-02-06

Total Pages: 617

ISBN-13: 1139435078

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The need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.

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