Error Detecting Codes

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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 Computers 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 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.

Error Detecting Codes Self Checking Circuits And Applications

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Author : John F. Wakerly
language : en
Publisher: North Holland
Release Date : 1978

Error Detecting Codes Self Checking Circuits And Applications written by John F. Wakerly and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Business & Economics categories.

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 Detecting Codes Self Checking Circuits And Applications

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Author : John F. Wakerly
language : en
Publisher:
Release Date : 1980

Error Detecting Codes Self Checking Circuits And Applications written by John F. Wakerly and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.

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.

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 Detecting Codes

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Author : Torleiv Kløve
language : en
Publisher: Springer
Release Date : 1995-09-30

Error Detecting Codes written by Torleiv Kløve and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 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.

Unidirectional Error Correcting Detecting Codes

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Author : Der J. Lin
language : en
Publisher:
Release Date : 1988

Unidirectional Error Correcting Detecting Codes written by Der J. Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Error-correcting codes (Information theory) categories.

An extensive theory of symmetric error control coding has been developed in the last few decades. The recently developed VLSI circuits, ROM, and RAM memories have given an impetus to the extension of error control coding to include asymmetric and unidirectional types of error control. The maximal numbers of unidirectional errors which can be detected by systematic codes using r checkbits are investigated. They are found for codes with k, the number of information bits, being equal to 2[superscript r] and 2[superscript r] + 1. The importance of their characteristic in unidirectional error detection is discussed. A new method of constructing a systematic t-error correcting/all-unidirectional error detecting(t-EC/AUED) code, which uses fewer checkbits than any of the previous methods, is developed. It is constructed by appending t + 1 check symbols to a systematic t-error correcting and (t+l)-error detecting code. Its decoding algorithm is developed. A bound on the number of checkbits for a systematic t-EC/AUED code is also discussed. Bose-Rao codes, which are the best known single error correcting/all-unidirectional error detecting(SEC/AUED) codes, are completely analyzed. The maximal Bose-Rao codes for a fixed weight and for all weights are found. Of course, the base group and the group element which make the Bose-Rao code maximal are found, too. The bounds on the size of SEC/AUED codes are discussed. Nonsystematic single error correcting/d-unidirectional error detecting codes are constructed. Three methods for constructing the systematic t-error correcting/d-unidirectional error detecting(t-EC/d-UED) codes are developed. From these, simple and efficient t-EC/(t+2)-UED codes are derived. The decoding algorithm for one of these methods, which can be applied to the other two methods with slight modification, is described. A lower bound on the number of checkbits for a systematic t-EC/d-UED code is derived. Finally, future research efforts are proposed.

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.