Download or read book Error Detecting Codes written by Torleiv Kløve and published by Springer Science & Business Media. This book was released on 1995-09-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Evaluation of Error detecting and Error correcting Codes written by Donald Matthew Syptak and published by . This book was released on 1963 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Codes for Error Detection written by Torleiv Klove and published by World Scientific. This book was released on 2007 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Error Correcting Codes second edition written by W. Wesley Peterson and published by National Geographic Books. This book was released on 1972-03-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error-Correcting Codes, by Professor Peterson, was originally published in 1961. Now, with E. J. Weldon, Jr., as his coauthor, Professor Peterson has extensively rewritten his material. The book contains essentially all of the material of the first edition; however, the authors state that because there has been so much new work published in error-correcting codes, the preparation of this second edition proved to be a much greater task than writing the original book. The major additions are the chapters on majority-logic codes, synchronization, and convolutional codes. Much new material has also been added to the chapters on important linear block codes and cyclic codes. The authors cite some highly regarded books on recent work done in Eastern Europe and an extensive bibliography on coding theory in the Soviet Union [sic]. In its much-expanded form, Error-Correcting Codes may be considered another valuable contribution to computer coding.
Download or read book Codes For Error Detection written by Torleiv Klove and published by World Scientific. This book was released on 2007-04-25 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Error Detecting and Error Correcting Codes written by Juan Miguel Sabater and published by . This book was released on 1962 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Error correcting Coding Theory written by Man Young Rhee and published by McGraw-Hill Companies. This book was released on 1989 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 238 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.
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.
Download or read book Linear Network Error Correction Coding written by Xuan Guang and published by Springer Science & Business Media. This book was released on 2014-03-21 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Global Variational Geometry written by Demeter Krupka and published by Elsevier. This book was released on 2000-04-01 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Download or read book Design Criteria for Error Detecting and Error Correcting Codes in Memory Subsystems written by Thomas Harold Howell and published by . This book was released on 1972 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Error correcting Codes written by William Wesley Peterson and published by MIT Press. This book was released on 1972 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Error Detecting Codes written by Torleiv Kløve and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
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 1989-05-31 with total page 316 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.
