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Author : William A. Geisel
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (317 download)
Download or read book Tutorial on Reed-Solomon Error Correction Coding written by William A. Geisel and published by . This book was released on 1990 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : National Aeronautics and Space Administration (NASA)
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781723468520
Total Pages : 144 pages
Book Rating : 4.4/5 (685 download)
Download or read book Tutorial on Reed-Solomon Error Correction Coding written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-23 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood. Geisel, William A. Johnson Space Center CODING; DECODING; ERROR ANALYSIS; FIELD THEORY (ALGEBRA); MAXIMUM LIKELIHOOD ESTIMATES; POLYNOMIALS; ERRORS; PROVING; SYMBOLS...
Author : Edward J. Weldon
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (314 download)
Download or read book Reed Solomon Error Correcting Codes written by Edward J. Weldon and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Venkatesan Guruswami
Publisher : Springer Science & Business Media
ISBN 13 : 3540240519
Total Pages : 354 pages
Book Rating : 4.5/5 (42 download)
Download or read book List Decoding of Error-Correcting Codes written by Venkatesan Guruswami and published by Springer Science & Business Media. This book was released on 2004-11-29 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a thoroughly revised and extended version of the author's PhD thesis, which was selected as the winning thesis of the 2002 ACM Doctoral Dissertation Competition. Venkatesan Guruswami did his PhD work at the MIT with Madhu Sudan as thesis adviser. Starting with the seminal work of Shannon and Hamming, coding theory has generated a 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 transmission errors efficiently. This book presents some spectacular new results in the area of decoding algorithms for error-correcting codes. Specificially, it shows how the notion of list-decoding can be applied to recover from far more errors, for a wide variety of error-correcting codes, than achievable before The style of the exposition is crisp and the enormous amount of information on combinatorial results, polynomial time list decoding algorithms, and applications is presented in well structured form.
Author : Martin Tomlinson
Publisher : Springer
ISBN 13 : 3319511033
Total Pages : 527 pages
Book Rating : 4.3/5 (195 download)
Download or read book Error-Correction Coding and Decoding written by Martin Tomlinson and published by Springer. This book was released on 2017-02-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.
Author : Robert H. Morelos-Zaragoza
Publisher : John Wiley & Sons
ISBN 13 : 0470035692
Total Pages : 278 pages
Book Rating : 4.4/5 (7 download)
Download or read book The Art of Error Correcting Coding written by Robert H. Morelos-Zaragoza and published by John Wiley & Sons. This book was released on 2006-07-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the first edition, which offered a practical introductory approach to the techniques of error concealment, this book, now fully revised and updated, provides a comprehensive treatment of the subject and includes a wealth of additional features. The Art of Error Correcting Coding, Second Edition explores intermediate and advanced level concepts as well as those which will appeal to the novice. All key topics are discussed, including Reed-Solomon codes, Viterbi decoding, soft-output decoding algorithms, MAP, log-MAP and MAX-log-MAP. Reliability-based algorithms GMD and Chase are examined, as are turbo codes, both serially and parallel concatenated, as well as low-density parity-check (LDPC) codes and their iterative decoders. Features additional problems at the end of each chapter and an instructor’s solutions manual Updated companion website offers new C/C ++programs and MATLAB scripts, to help with the understanding and implementation of basic ECC techniques Easy to follow examples illustrate the fundamental concepts of error correcting codes Basic analysis tools are provided throughout to help in the assessment of the error performance block and convolutional codes of a particular error correcting coding (ECC) scheme for a selection of the basic channel models This edition provides an essential resource to engineers, computer scientists and graduate students alike for understanding and applying ECC techniques in the transmission and storage of digital information.
Author : Jørn Justesen
Publisher : European Mathematical Society
ISBN 13 : 9783037190012
Total Pages : 210 pages
Book Rating : 4.1/5 (9 download)
Download or read book A Course in Error-correcting Codes written by Jørn Justesen and published by European Mathematical Society. This book was released on 2004 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as a text for a course aimed at advanced undergraduates. Chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts.
Author : Richard E. Blahut
Publisher : Cambridge University Press
ISBN 13 : 1139435078
Total Pages : 617 pages
Book Rating : 4.1/5 (394 download)
Download or read book Algebraic Codes for Data Transmission written by Richard E. Blahut and published by Cambridge University Press. This book was released on 2003-02-06 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Lin Shu
Publisher : Pearson Education India
ISBN 13 : 9788131734407
Total Pages : 1276 pages
Book Rating : 4.7/5 (344 download)
Download or read book Error Control Coding written by Lin Shu and published by Pearson Education India. This book was released on 2011 with total page 1276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Scott A. Vanstone
Publisher : Springer Science & Business Media
ISBN 13 : 1475720327
Total Pages : 297 pages
Book Rating : 4.4/5 (757 download)
Download or read book An Introduction to Error Correcting Codes with Applications written by Scott A. Vanstone and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : A. Houghton
Publisher : Springer Science & Business Media
ISBN 13 : 1461515092
Total Pages : 249 pages
Book Rating : 4.4/5 (615 download)
Download or read book Error Coding for Engineers written by A. Houghton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error Coding for Engineers provides a useful tool for practicing engineers, students, and researchers, focusing on the applied rather than the theoretical. It describes the processes involved in coding messages in such a way that, if errors occur during transmission or storage, they are detected and, if necessary, corrected. Very little knowledge beyond a basic understanding of binary manipulation and Boolean algebra is assumed, making the subject accessible to a broad readership including non-specialists. The approach is tutorial: numerous examples, illustrations, and tables are included, along with over 30 pages of hands-on exercises and solutions. Error coding is essential in many modern engineering applications. Engineers involved in communications design, DSP-based applications, IC design, protocol design, storage solutions, and memory product design are among those who will find the book to be a valuable reference. Error Coding for Engineers is also suitable as a text for basic and advanced university courses in communications and engineering.
Author : Sarah Edge Mann
Publisher :
ISBN 13 :
Total Pages : 286 pages
Book Rating : 4.:/5 (858 download)
Download or read book The Original View of Reed-Solomon Coding and the Welch-Berlekamp Decoding Algorithm written by Sarah Edge Mann and published by . This book was released on 2013 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reed-Solomon codes are a class of maximum distance separable error correcting codes with known fast error correction algorithms. They have been widely used to assure data integrity for stored data on compact discs, DVDs, and in RAID storage systems, for digital communications channels such as DSL internet connections, and for deep space communications on the Voyager mission. The recent explosion of storage needs for "Big Data'' has generated renewed interest in large storage systems with extended error correction capacity. Reed-Solomon codes have been suggested as one potential solution. This dissertation reviews the theory of Reed-Solomon codes from the perspective taken in Reed and Solomon's original paper on them. It then derives the Welch-Berlekamp algorithm for solving certain polynomial equations, and connects this algorithm to the problem of error correction. The discussion is mathematically rigorous, and provides a complete and consistent discussion of the error correction process. Numerous algorithms for encoding, decoding, erasure recovery, error detection, and error correction are provided and their computational cost is analyzed and discussed thus allowing this dissertation to serve as a manual for engineers interested in implementing Reed-Solomon coding.
Author : Benjamin Arazi
Publisher : MIT Press
ISBN 13 : 9780262010986
Total Pages : 232 pages
Book Rating : 4.0/5 (19 download)
Download or read book A Commonsense Approach to the Theory of Error Correcting Codes written by Benjamin Arazi and published by MIT Press. This book was released on 1988 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : IEEE Communications Society
Publisher : Institute of Electrical & Electronics Engineers(IEEE)
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.F/5 ( download)
Download or read book Reed-Solomon Codes and Their Applications written by IEEE Communications Society and published by Institute of Electrical & Electronics Engineers(IEEE). This book was released on 1994 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reed-Solomon codes provide critical error control for many different types of digital communications systems, including those on the Voyager spacecraft and in CD players. This collection of 13 articles from leading researchers in the field provides a comprehensive overview of the history and practical applications--some never before published--of these important codes.
Author : N.J.A. Sloane
Publisher : Springer
ISBN 13 : 3709128641
Total Pages : 78 pages
Book Rating : 4.7/5 (91 download)
Download or read book A Short Course on Error Correcting Codes written by N.J.A. Sloane and published by Springer. This book was released on 2014-05-04 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Houghton
Publisher : Springer Science & Business Media
ISBN 13 : 1461304474
Total Pages : 259 pages
Book Rating : 4.4/5 (613 download)
Download or read book The Engineer’s Error Coding Handbook written by A. Houghton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error coding is a fascinating subject as much, if not more so, as it is an indispensable part of modem engineering systems. Unfortunately, in a bid to remain general and to create a solid foundation upon which to build, many books on this subject are out of the reach of those with more engineering-based, or non-mathematical backgrounds. This is a pity because in many cases the maths is tractable with few and simple rules. If we are content to believe that it works, and let others worry about the deeper mysteries of how or why, then with a little practice the design and implementation of practical error coding systems becomes straightforward. In this text I have attempted to reveal the useful kernel of the subject, removing the shell of terms and proofs that usually surrounds it. Being somewhat empirical in nature ( an empiricist), and occasionally heard to quote the adage, 'if it works twice it's a law', my explanations take this form. For many, including myself, abstract ideas are often better grasped by practical illustration than from yards of theory.
Author : Grigorii Kabatiansky
Publisher : John Wiley & Sons
ISBN 13 : 0470867566
Total Pages : 288 pages
Book Rating : 4.4/5 (78 download)
Download or read book Error Correcting Coding and Security for Data Networks written by Grigorii Kabatiansky and published by John Wiley & Sons. This book was released on 2005-10-31 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other. In this fresh approach, the authors consider the data network as a superchannel (a multi-layered entity) which allows error correcting coding to be evaluated as it is applied to a number of network layers as a whole. By exposing the problems of applying error correcting coding in data networks, and by discussing coding theory and its applications, this original technique shows how to correct errors in the network through joint coding at different network layers. Discusses the problem of reconciling coding applied to different layers using a superchannel approach Includes thorough coverage of all the key codes: linear block codes, Hamming, BCH and Reed-Solomon codes, LDPC codes decoding, as well as convolutional, turbo and iterative coding Considers new areas of application of error correcting codes such as transport coding, code-based cryptosystems and coding for image compression Demonstrates how to use error correcting coding to control such important data characteristics as mean message delay Provides theoretical explanations backed up by numerous real-world examples and practical recommendations Features a companion website containing additional research results including new constructions of LDPC codes, joint error-control coding and synchronization, Reed-Muller codes and their list decoding By progressing from theory through to practical problem solving, this resource contains invaluable advice for researchers, postgraduate students, engineers and computer scientists interested in data communications and applications of coding theory.
