An Introduction To Error Correcting Codes With Applications

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An Introduction to Error Correcting Codes with Applications

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Author : Scott A. Vanstone
Publisher : Springer Science & Business Media
ISBN 13 : 1475720327
Total Pages : 297 pages
Book Rating : 4.4/5 (757 download)

Book Synopsis An Introduction to Error Correcting Codes with Applications by : Scott A. Vanstone

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.

Error-Correcting Linear Codes

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Author : Anton Betten
Publisher : Springer Science & Business Media
ISBN 13 : 3540317031
Total Pages : 819 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Error-Correcting Linear Codes by : Anton Betten

Download or read book Error-Correcting Linear Codes written by Anton Betten and published by Springer Science & Business Media. This book was released on 2006-09-21 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

Error Correcting Codes

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Author : D J. Baylis
Publisher : Routledge
ISBN 13 : 1351449842
Total Pages : 232 pages
Book Rating : 4.3/5 (514 download)

Book Synopsis Error Correcting Codes by : D J. Baylis

Download or read book Error Correcting Codes written by D J. Baylis and published by Routledge. This book was released on 2018-05-11 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.

A Commonsense Approach to the Theory of Error Correcting Codes

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Author : Benjamin Arazi
Publisher : MIT Press
ISBN 13 : 9780262010986
Total Pages : 232 pages
Book Rating : 4.0/5 (19 download)

Book Synopsis A Commonsense Approach to the Theory of Error Correcting Codes by : Benjamin Arazi

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.

Fundamentals of Error-Correcting Codes

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Author : W. Cary Huffman
Publisher : Cambridge University Press
ISBN 13 : 1139439502
Total Pages : 668 pages
Book Rating : 4.1/5 (394 download)

Book Synopsis Fundamentals of Error-Correcting Codes by : W. Cary Huffman

Download or read book Fundamentals of Error-Correcting Codes written by W. Cary Huffman and published by Cambridge University Press. This book was released on 2010-02-18 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.

Error Correction Coding

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Author : Todd K. Moon
Publisher : John Wiley & Sons
ISBN 13 : 0471648000
Total Pages : 800 pages
Book Rating : 4.4/5 (716 download)

Book Synopsis Error Correction Coding by : Todd K. Moon

Download or read book Error Correction Coding written by Todd K. Moon and published by John Wiley & Sons. This book was released on 2005-06-06 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Course in Algebraic Error-Correcting Codes

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Author : Simeon Ball
Publisher : Springer Nature
ISBN 13 : 3030411532
Total Pages : 185 pages
Book Rating : 4.0/5 (34 download)

Book Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Ball

Download or read book A Course in Algebraic Error-Correcting Codes written by Simeon Ball and published by Springer Nature. This book was released on 2020-05-08 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Foundations of Coding

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Author : Jiri Adamek
Publisher : John Wiley & Sons
ISBN 13 : 1118031512
Total Pages : 352 pages
Book Rating : 4.1/5 (18 download)

Book Synopsis Foundations of Coding by : Jiri Adamek

Download or read book Foundations of Coding written by Jiri Adamek and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

An Introduction to Error-correcting Codes

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Author : Shu Lin
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.3/5 (97 download)

Book Synopsis An Introduction to Error-correcting Codes by : Shu Lin

Download or read book An Introduction to Error-correcting Codes written by Shu Lin and published by Prentice Hall. This book was released on 1970 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Codes, Kodierung (Telegrafie) ; Kodierung, Datendarstellung, Bit, Byte (EDV).

The Theory of Error Correcting Codes

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Author : Florence Jessie MacWilliams
Publisher :
ISBN 13 :
Total Pages : 762 pages
Book Rating : 4.:/5 (163 download)

Book Synopsis The Theory of Error Correcting Codes by : Florence Jessie MacWilliams

Download or read book The Theory of Error Correcting Codes written by Florence Jessie MacWilliams and published by . This book was released on 1978 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A First Course in Coding Theory

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Author : Raymond Hill
Publisher : Oxford University Press
ISBN 13 : 9780198538035
Total Pages : 268 pages
Book Rating : 4.5/5 (38 download)

Book Synopsis A First Course in Coding Theory by : Raymond Hill

Download or read book A First Course in Coding Theory written by Raymond Hill and published by Oxford University Press. This book was released on 1986 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

A Course in Error-correcting Codes

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Author : Jørn Justesen
Publisher : European Mathematical Society
ISBN 13 : 9783037190012
Total Pages : 210 pages
Book Rating : 4.1/5 (9 download)

Book Synopsis A Course in Error-correcting Codes by : Jørn Justesen

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.

Fundamentals of Classical and Modern Error-Correcting Codes

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Author : Shu Lin
Publisher : Cambridge University Press
ISBN 13 : 1316512622
Total Pages : 843 pages
Book Rating : 4.3/5 (165 download)

Book Synopsis Fundamentals of Classical and Modern Error-Correcting Codes by : Shu Lin

Download or read book Fundamentals of Classical and Modern Error-Correcting Codes written by Shu Lin and published by Cambridge University Press. This book was released on 2021-12-09 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.

The Art of Error Correcting Coding

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Author : Robert H. Morelos-Zaragoza
Publisher : John Wiley & Sons
ISBN 13 : 0470035692
Total Pages : 278 pages
Book Rating : 4.4/5 (7 download)

Book Synopsis The Art of Error Correcting Coding by : Robert H. Morelos-Zaragoza

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.

List Decoding of Error-Correcting Codes

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Author : Venkatesan Guruswami
Publisher : Springer Science & Business Media
ISBN 13 : 3540240519
Total Pages : 354 pages
Book Rating : 4.5/5 (42 download)

Book Synopsis List Decoding of Error-Correcting Codes by : Venkatesan Guruswami

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.

Lattices and Codes

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Author : Wolfgang Ebeling
Publisher : Springer Science & Business Media
ISBN 13 : 3322900142
Total Pages : 205 pages
Book Rating : 4.3/5 (229 download)

Book Synopsis Lattices and Codes by : Wolfgang Ebeling

Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 2nd edition numerous corrections have been made. More basic material has been included to make the text even more self-contained. A new section on the automorphism group of the Leech lattice has been added. Some hints to new results have been incorporated. With several new exercises.

Theory and Practice of Error Control Codes

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Author : Richard E. Blahut
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Theory and Practice of Error Control Codes by : Richard E. Blahut

Download or read book Theory and Practice of Error Control Codes written by Richard E. Blahut and published by Addison Wesley Publishing Company. This book was released on 1983 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: