Reed Solomon Error Correcting Codes
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An Introduction To Error Correcting Codes With Applications
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Author : Scott A. Vanstone
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
An Introduction To Error Correcting Codes With Applications written by Scott A. Vanstone 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 2013-04-18 with Technology & Engineering categories.
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.
Fundamentals Of Error Correcting Codes
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Author : W. Cary Huffman
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-26
Fundamentals Of Error Correcting Codes written by W. Cary Huffman 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 2003-06-26 with Computers categories.
In-depth introduction to coding theory from both an engineering and mathematical viewpoint.
Error Control Coding For Data Networks
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Author : Irving S. Reed
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Error Control Coding For Data Networks written by Irving S. Reed 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 2012-12-06 with Computers categories.
The purpose of Error-Control Coding for Data Networks is to provide an accessible and comprehensive overview of the fundamental techniques and practical applications of the error-control coding needed by students and engineers. An additional purpose of the book is to acquaint the reader with the analytical techniques used to design an error-control coding system for many new applications in data networks. Error~control coding is a field in which elegant theory was motivated by practical problems so that it often leads to important useful advances. Claude Shannon in 1948 proved the existence of error-control codes that, under suitable conditions and at rates less than channel capacity, would transmit error-free information for all practical applications. The first practical binary codes were introduced by Richard Hamming and Marcel Golay from which the drama and excitement have infused researchers and engineers in digital communication and error-control coding for more than fifty years. Nowadays, error-control codes are being used in almost all modem digital electronic systems and data networks. Not only is coding equipment being implemented to increase the energy and bandwidth efficiency of communication systems, but coding also provides innovative solutions to many related data-networking problems.
Error Correction Coding
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Author : Todd K. Moon
language : en
Publisher: John Wiley & Sons
Release Date : 2005-06-06
Error Correction Coding written by Todd K. Moon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-06 with Computers categories.
An unparalleled learning tool and guide to error correction coding Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy. Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes. This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems. Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists.
A Commonsense Approach To The Theory Of Error Correcting Codes
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Author : Benjamin Arazi
language : en
Publisher: MIT Press
Release Date : 1988
A Commonsense Approach To The Theory Of Error Correcting Codes written by Benjamin Arazi and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Computers categories.
Teaching the theory of error correcting codes on an introductory level is a difficulttask. The theory, which has immediate hardware applications, also concerns highly abstractmathematical concepts. This text explains the basic circuits in a refreshingly practical way thatwill appeal to undergraduate electrical engineering students as well as to engineers and techniciansworking in industry.Arazi's truly commonsense approach provides a solid grounding in the subject,explaining principles intuitively from a hardware perspective. He fully covers error correctiontechniques, from basic parity check and single error correction cyclic codes to burst errorcorrecting codes and convolutional codes. All this he presents before introducing Galois fieldtheory - the basic algebraic treatment and theoretical basis of the subject, which usually appearsin the opening chapters of standard textbooks. One entire chapter is devoted to specific practicalissues, such as Reed-Solomon codes (used in compact disc equipment), and maximum length sequences(used in various fields of communications). The basic circuits explained throughout the book areredrawn and analyzed from a theoretical point of view for readers who are interested in tackling themathematics at a more advanced level.Benjamin Arazi is an Associate Professor in the Department ofElectrical and Computer Engineering at the Ben-Gurion University of the Negev. His book is includedin the Computer Systems Series, edited by Herb Schwetman.
Tutorial On Reed Solomon Error Correction Coding
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Author : William A. Geisel
language : en
Publisher:
Release Date : 1990
Tutorial On Reed Solomon Error Correction Coding written by William A. Geisel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Error-correcting codes (Information theory) categories.
List Decoding Of Error Correcting Codes
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Author : Venkatesan Guruswami
language : en
Publisher: Springer
Release Date : 2004-11-29
List Decoding Of Error Correcting Codes written by Venkatesan Guruswami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Computers categories.
How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”. This theory has traditionally gone hand in hand with the algorithmic theory of “decoding” that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.
Reed Solomon Codes And Their Applications
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Author : Stephen B. Wicker
language : en
Publisher: John Wiley & Sons
Release Date : 1999-10-12
Reed Solomon Codes And Their Applications written by Stephen B. Wicker and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-12 with Technology & Engineering categories.
Electrical Engineering/Communications/Information Theory "The Berlekamp article alone will make this book worth having." --David Forney, Vice President, Motorola Codex Reed-Solomon Codes and Their Applications Edited by Stephen B. Wicker, Georgia Institute of Technology and Vijay K. Bhargava, University of Victoria On the Voyager spacecraft, they were responsible for sending clear pictures of the planets back to earth. They have also played a key role in the digital audio revolution. They are Reed-Solomon error codes: the extremely powerful codes that provide critical error control for many different types of digital communications systems. This outstanding collection of thirteen original articles written by leading researchers in the field provides a uniquely comprehensive overview of the history and practical applications--some never before published--of these important codes. Key features include: * Thirteen original articles from leading researchers in the field, with a historical overview by Reed and Solomon * An explanation of how Reed-Solomon codes were used in the Voyager spacecraft and how they are currently used in the compact disc player * Specific applications for digital audio, data transfer over mobile radio, satellite communications, spread spectrum systems, and more * New techniques for improving the performance of your own communications systems This book will be of interest to design and research engineers in the telecommunications field, particularly those in the aerospace/satellite and mobile radio industries. It is also well-suited for use as an advanced-level textbook on the subject of error control coding. Books of Related Interest from IEEE Press Clauide Elwood Shannon: Collected Papers Edited by N. J. A. Sloane and A. D. Wyner. AT&T Bell Labs The first published collection of papers by Claude E. Shannon, including his seminal article "The Mathematical Theory of Communication." 1993 Hardcover 968 pp IEEE Order Number PC0331-9 ISBN 0-7803-0434-9 Multiple Access Communications: Foundations for Emerging Technologies Edited by Norman Abramson, University of Hawaii at Manoa The first book to explain the connection between spread spectrum and ALOHA channels, providing a collection of key developments in the theory and practice of multiple user communications channels. 1993 Hardcover 528pp IEEE Order Number PC0287-3 ISBN 0-87942-292-0
Error Correction Codes For Non Volatile Memories
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Author : Rino Micheloni
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-03
Error Correction Codes For Non Volatile Memories written by Rino Micheloni 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 2008-06-03 with Technology & Engineering categories.
Nowadays it is hard to find an electronic device which does not use codes: for example, we listen to music via heavily encoded audio CD's and we watch movies via encoded DVD's. There is at least one area where the use of encoding/decoding is not so developed, yet: Flash non-volatile memories. Flash memory high-density, low power, cost effectiveness, and scalable design make it an ideal choice to fuel the explosion of multimedia products, like USB keys, MP3 players, digital cameras and solid-state disk. In ECC for Non-Volatile Memories the authors expose the basics of coding theory needed to understand the application to memories, as well as the relevant design topics, with reference to both NOR and NAND Flash architectures. A collection of software routines is also included for better understanding. The authors form a research group (now at Qimonda) which is the typical example of a fruitful collaboration between mathematicians and engineers.
Reed Solomon Error Correcting Codes
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Author : Edward J. Weldon
language : en
Publisher:
Release Date : 1983
Reed Solomon Error Correcting Codes written by Edward J. Weldon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.