Algebraic Codes For Data Transmission
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Algebraic Codes For Data Transmission
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Author : Richard E. Blahut
language : en
Publisher: Cambridge University Press
Release Date : 2003-02-06
Algebraic Codes For Data Transmission written by Richard E. Blahut and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-06 with Technology & Engineering categories.
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.
Algebraic Codes On Lines Planes And Curves
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Author : Richard E. Blahut
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-03
Algebraic Codes On Lines Planes And Curves written by Richard E. Blahut and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-03 with Technology & Engineering categories.
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.
Algebraic And Stochastic Coding Theory
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Author : Dave K. Kythe
language : en
Publisher: CRC Press
Release Date : 2017-07-28
Algebraic And Stochastic Coding Theory written by Dave K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Computers categories.
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.
Algebraic Number Theory And Code Design For Rayleigh Fading Channels
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Author : Frédérique Oggier
language : en
Publisher: Now Publishers Inc
Release Date : 2004
Algebraic Number Theory And Code Design For Rayleigh Fading Channels written by Frédérique Oggier and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Algebraic Number Theory and Code Design for Rayleigh Fading Channels provides an overview of algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory.
Introduction To Coding Theory
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Author : Jurgen Bierbrauer
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Introduction To Coding Theory written by Jurgen Bierbrauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.
Neutrosophic Quadruple Algebraic Codes Over Z2 And Their Properties
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Author : Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Quadruple Algebraic Codes Over Z2 And Their Properties written by Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper we for the rst time develop, de ne and describe a new class of algebraic codes using Neutrosophic Quadruples which uses the notion of known value, and three unknown triplets (T; I; F) where T is the truth value, I is the indeterminate and F is the false value.
Error Correcting Coding Theory
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Author : Man Young Rhee
language : en
Publisher: McGraw-Hill Companies
Release Date : 1989
Error Correcting Coding Theory written by Man Young Rhee and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.
Introduction To Coding Theory
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Author : Juergen Bierbrauer
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2004-08-17
Introduction To Coding Theory written by Juergen Bierbrauer and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-17 with Mathematics categories.
Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.
Codes Cryptology And Curves With Computer Algebra
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Author : Ruud Pellikaan
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-02
Codes Cryptology And Curves With Computer Algebra written by Ruud Pellikaan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Language Arts & Disciplines categories.
Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.
Selected Unsolved Problems In Coding Theory
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Author : David Joyner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-26
Selected Unsolved Problems In Coding Theory written by David Joyner 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 2011-08-26 with Mathematics categories.
Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.