Codes For Error Detection
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Codes For Error Detection
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Author : Torleiv Klove
language : en
Publisher: World Scientific
Release Date : 2007
Codes For Error Detection written by Torleiv Klove and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
There are two basic methods of error control for communication, both involving coding of the messages. With forward error correction, the codes are used to detect and correct errors. In a repeat request system, the codes are used to detect errors and, if there are errors, request a retransmission. Error detection is usually much simpler to implement than error correction and is widely used. However, it is given a very cursory treatment in almost all textbooks on coding theory. Only a few older books are devoted to error detecting codes. This book begins with a short introduction to the theory of block codes with emphasis on the parts important for error detection. The weight distribution is particularly important for this application and is treated in more detail than in most books on error correction. A detailed account of the known results on the probability of undetected error on the q-ary symmetric channel is also given.
Error Correcting Codes
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Author : D J. Baylis
language : en
Publisher: Routledge
Release Date : 2018-05-11
Error Correcting Codes written by D J. Baylis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.
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.
Error Correcting Codes
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Author : William Wesley Peterson
language : en
Publisher: MIT Press
Release Date : 1972
Error Correcting Codes written by William Wesley Peterson and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Computers categories.
The coding problem; Introduction to algebra; Linear codes; Error correction capabilities of linear codes; Important linear block codes; Polynomial rings and galois fields; Linear switching circuits; Cyclic codes; Bose-chaudhuri-hocquenghem codes; Arithmetic codes.
Error Correction Coding And Decoding
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Author : Martin Tomlinson
language : en
Publisher: Springer
Release Date : 2017-02-21
Error Correction Coding And Decoding written by Martin Tomlinson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-21 with Technology & Engineering categories.
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.
Error Detecting Codes
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Author : Torleiv Kløve
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Error Detecting Codes written by Torleiv Kløve 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 Technology & Engineering categories.
Error detecting codes are very popular for error control in practical systems for two reasons. First, such codes can be used to provide any desired reliability of communication over any noisy channel. Second, implementation is usually much simpler than for a system using error correcting codes. To consider a particular code for use in such a system, it is very important to be able to calculate or estimate the probability of undetected error. For the binary symmetric channel, the probability of undetected error can be expressed in terms of the weight distribution of the code. The first part of the book gives a detailed description of all known methods to calculate or estimate the probability of undetected error, for the binary symmetric channel in particular, but a number of other channel models are also considered. The second part of the book describes a number of protocols for feedback communication systems (ARQ systems), with methods for optimal choice of error detecting codes for the protocols. Results have been collected from many sources and given a unified presentation. The results are presented in a form which make them accessible to the telecommunication system designer as well as the coding theory researcher and student. The system designer may find the presentation of CRC codes as well as the system performance analysis techniques particularly useful. The coding theorist will find a detailed account of a part of coding theory which is usually just mentioned in most text books and which contains a number of interesting and useful results as well as many challenging open problems. Audience: Essential for students, practitioners and researchers working in communications and coding theory. An excellent text for an advanced course on the subject.
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.
Practical Error Correction Design For Engineers
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Author : Neal Glover
language : en
Publisher:
Release Date : 1991
Practical Error Correction Design For Engineers written by Neal Glover and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Error-correcting codes (Information theory) categories.
Fundamentals Of Error Correcting Codes
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Author : W. Cary Huffman
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-18
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 2010-02-18 with Technology & Engineering categories.
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.
Linear Network Error Correction Coding
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Author : Xuan Guang
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-21
Linear Network Error Correction Coding written by Xuan Guang 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 2014-03-21 with Computers categories.
There are two main approaches in the theory of network error correction coding. In this SpringerBrief, the authors summarize some of the most important contributions following the classic approach, which represents messages by sequences similar to algebraic coding, and also briefly discuss the main results following the other approach, that uses the theory of rank metric codes for network error correction of representing messages by subspaces. This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions. Distances and weights are defined in order to characterize the discrepancy of these two vectors and to measure the seriousness of errors. Similar to classical error-correcting codes, the authors also apply the minimum distance decoding principle to LNEC codes at each sink node, but use distinct distances. For this decoding principle, it is shown that the minimum distance of a LNEC code at each sink node can fully characterize its error-detecting, error-correcting and erasure-error-correcting capabilities with respect to the sink node. In addition, some important and useful coding bounds in classical coding theory are generalized to linear network error correction coding, including the Hamming bound, the Gilbert-Varshamov bound and the Singleton bound. Several constructive algorithms of LNEC codes are presented, particularly for LNEC MDS codes, along with an analysis of their performance. Random linear network error correction coding is feasible for noncoherent networks with errors. Its performance is investigated by estimating upper bounds on some failure probabilities by analyzing the information transmission and error correction. Finally, the basic theory of subspace codes is introduced including the encoding and decoding principle as well as the channel model, the bounds on subspace codes, code construction and decoding algorithms.
Advanced Hardware Design For Error Correcting Codes
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Author : Cyrille Chavet
language : en
Publisher: Springer
Release Date : 2014-10-30
Advanced Hardware Design For Error Correcting Codes written by Cyrille Chavet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-30 with Technology & Engineering categories.
This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques. Advanced Hardware Design for Error Correcting Codes includes a foreword by Claude Berrou.