algebraic codes for data transmission

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Algebraic Codes For Data Transmission

Author : Richard E. Blahut
ISBN : 9781139435079
Genre : Technology & Engineering
File Size : 64. 9 MB
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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.

Algebraic Codes On Lines Planes And Curves

Author : Richard E. Blahut
ISBN : 9781139469463
Genre : Technology & Engineering
File Size : 55. 82 MB
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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

Author : Ruud Pellikaan
ISBN : 9781108547826
Genre : Mathematics
File Size : 42. 73 MB
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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.

Theory And Practice Of Error Control Codes

Author : Richard E. Blahut
ISBN : UOM:39015040304217
Genre : Reference
File Size : 73. 30 MB
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Applied Algebra

Author : Darel W. Hardy
ISBN : 9781420071436
Genre : Mathematics
File Size : 35. 42 MB
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Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.

Algebraic Coding Theory

Author : Elwyn R Berlekamp
ISBN : 9789814635912
Genre :
File Size : 40. 51 MB
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This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory", originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose–Chaudhuri–Hocquenghem codes that subsequently became known as the Berlekamp–Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes. Selected chapters of the book became a standard graduate textbook. Both practicing engineers and scholars will find this book to be of great value. Contents:Basic Binary CodesArithmetic Operations Modulo An Irreducible Binary PolynomialThe Number of Irreducible q-ary Polynomials of Given DegreeThe Structure of Finite FieldsCyclic Binary CodesThe Factorization of Polynomials Over Finite FieldsBinary BCH Codes for Correcting Multiple ErrorsNonbinary CodingNegacyclic Codes for the Lee MetricGorenstein-Zierler Generalized Nonbinary BCH Codes for the Hamming MetricLinearized Polynomials and Affine PolynomialsThe Enumeration of Information Symbols in BCH CodesThe Information Rate of the Optimum CodesCodes Derived by Modifying or Combining Other CodesOther Important Coding and Decoding MethodsWeight EnumeratorsAppendices and References Readership: Researchers in coding theory and cryptography, algebra and number theory, and software engineering. Key Features:A classic monograph and reference book on Coding Theory and Cryptography written by a revered scholar long known for his work in coding theoryContains several theorems created by the author that have been respected for 40 yearsKeywords:Coding Theory;Binary Codes;Irreducible Q-ary Polynomial;Error-Correcting Codes;BCH Codes;Berlekamp's Algorithm;Finite Fields

Introduction To Coding Theory

Author : Ron Roth
ISBN : 0521845041
Genre : Computers
File Size : 77. 18 MB
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This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

Algebraic And Stochastic Coding Theory

Author : Dave K. Kythe
ISBN : 9781351832458
Genre : Computers
File Size : 23. 76 MB
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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.

Modem Theory

Author : Richard E. Blahut
ISBN : 9780521780148
Genre : Technology & Engineering
File Size : 42. 30 MB
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This detailed introduction presents the theory of digital modulation and coding underpinning the modern design of modems for telecommunications. From baseband and passband modulation and demodulation to sequence estimation, turbo codes, and the Viterbi algorithm, a wide range of key topics is covered, whilst end-of-chapter exercises test students' understanding throughout.

Algebraic Methods For Signal Processing And Communications Coding

Author : Richard E. Blahut
ISBN : 9781461228264
Genre : Technology & Engineering
File Size : 85. 7 MB
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Algorithms for computation are a central part of both digital signal pro cessing and decoders for error-control codes and the central algorithms of the two subjects share many similarities. Each subject makes extensive use of the discrete Fourier transform, of convolutions, and of algorithms for the inversion of Toeplitz systems of equations. Digital signal processing is now an established subject in its own right; it no longer needs to be viewed as a digitized version of analog signal process ing. Algebraic structures are becoming more important to its development. Many of the techniques of digital signal processing are valid in any algebraic field, although in most cases at least part of the problem will naturally lie either in the real field or the complex field because that is where the data originate. In other cases the choice of field for computations may be up to the algorithm designer, who usually chooses the real field or the complex field because of familiarity with it or because it is suitable for the particular application. Still, it is appropriate to catalog the many algebraic fields in a way that is accessible to students of digital signal processing, in hopes of stimulating new applications to engineering tasks.

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