Error Correcting Linear Codes

Error Correcting Linear Codes

This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering.

Author: Anton Betten

Publisher: Springer Science & Business Media

ISBN: 9783540317036

Category: Mathematics

Page: 798

View: 962

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.
Categories: Mathematics

Error correcting Codes

Error correcting Codes

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 ...

Author: William Wesley Peterson

Publisher: MIT Press

ISBN: 0262160390

Category: Computers

Page: 560

View: 611

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.
Categories: Computers

Error Correcting Codes

Error Correcting Codes

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 ...

Author: D J. Baylis

Publisher: Routledge

ISBN: 9781351449847

Category: Mathematics

Page: 232

View: 481

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.
Categories: Mathematics

A Course in Algebraic Error Correcting Codes

A Course in Algebraic Error Correcting Codes

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.

Author: Simeon Ball

Publisher: Springer Nature

ISBN: 9783030411534

Category: Mathematics

Page: 177

View: 506

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.
Categories: Mathematics

Error Correcting Linear Codes

Error Correcting Linear Codes

This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering.

Author: Anton Betten

Publisher: Springer

ISBN: 3540814442

Category: Mathematics

Page: 798

View: 334

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.
Categories: Mathematics

Linear Network Error Correction Coding

Linear Network Error Correction Coding

This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions.

Author: Xuan Guang

Publisher: Springer Science & Business Media

ISBN: 9781493905881

Category: Computers

Page: 107

View: 391

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.
Categories: Computers

Foundations of Coding

Foundations of Coding

The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

Author: Jiri Adamek

Publisher: John Wiley & Sons

ISBN: 9781118031513

Category: Computers

Page: 352

View: 377

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.
Categories: Computers

Error Correcting Coding and Security for Data Networks

Error Correcting Coding and Security for Data Networks

Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other.

Author: Grigorii Kabatiansky

Publisher: John Wiley & Sons

ISBN: 9780470867563

Category: Technology & Engineering

Page: 288

View: 295

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.
Categories: Technology & Engineering

A Practical Guide to Error Control Coding Using MATLAB

A Practical Guide to Error Control Coding Using MATLAB

This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes.You find clear guidance on code construction, decoding algorithms, and error correcting performances.

Author: Yuan Jiang

Publisher: Artech House

ISBN: 9781608070893

Category: Computer programming

Page: 292

View: 174

This practical resource provides you with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. The goal of error control coding is to encode information in such a way that even if the channel (or storage medium) introduces errors, the receiver can correct the errors and recover the original transmitted information. This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes.You find clear guidance on code construction, decoding algorithms, and error correcting performances. Moreover, this unique book introduces computer simulations integrally to help you master key concepts. Including a companion DVD with MATLAB programs and supported with over 540 equations, this hands-on reference provides you with an in-depth treatment of a wide range of practical implementation issues.
Categories: Computer programming

Introduction to the Theory of Error correcting Codes

Introduction to the Theory of Error correcting Codes

An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book.

Author: Vera Pless

Publisher: Wiley-Interscience

ISBN: UOM:39015015706206

Category: Error-correcting codes (Information theory).

Page: 201

View: 994

An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book. It considers such codes as Hamming codes and Golay codes, correction of double errors, use of finite fields, cyclic codes, BCH codes and weight distributions, as well as design of codes. In this second edition, the author includes more material on non-binary code and cyclic codes. In addition some proofs have been simplified and there are many more examples and problems. The text has been aimed at mathematicians, electrical engineers and computer scientists.
Categories: Error-correcting codes (Information theory).

An Introduction to Error Correcting Codes with Applications

An Introduction to Error Correcting Codes with Applications

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 ...

Author: Scott A. Vanstone

Publisher: Springer Science & Business Media

ISBN: 9781475720327

Category: Technology & Engineering

Page: 289

View: 291

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.
Categories: Technology & Engineering

Fundamentals of Error Correcting Codes

Fundamentals of Error Correcting Codes

Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint.

Author: W. Cary Huffman

Publisher: Cambridge University Press

ISBN: 1139439502

Category: Technology & Engineering

Page:

View: 517

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.
Categories: Technology & Engineering

List Decoding of Error Correcting Codes

List Decoding of Error Correcting Codes

This book presents some spectacular new results in the area of decoding algorithms for error-correcting codes.

Author: Venkatesan Guruswami

Publisher: Springer Science & Business Media

ISBN: 3540240519

Category: Computers

Page: 350

View: 287

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.
Categories: Computers

Block Error Correcting Codes

Block Error Correcting Codes

The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose.

Author: Sebastian Xambo-Descamps

Publisher: Springer Science & Business Media

ISBN: 9783642189975

Category: Computers

Page: 266

View: 706

Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of the theory of block error-correcting codes together, in mutual reinforcement, with computational discussions, implementations and examples of all relevant concepts, functions and algorithms. This combined approach facilitates the reading and understanding of the subject. The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose.
Categories: Computers

Error correcting Codes and Finite Fields

Error correcting Codes and Finite Fields

Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.

Author: Oliver Pretzel

Publisher: Oxford University Press

ISBN: STANFORD:36105000110978

Category: Computers

Page: 398

View: 344

Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.
Categories: Computers

An Introduction to Error correcting Codes

An Introduction to Error correcting Codes

Codes, Kodierung (Telegrafie) ; Kodierung, Datendarstellung, Bit, Byte (EDV).

Author: Shu Lin

Publisher: Prentice Hall

ISBN: UOM:39076006526870

Category: Codes correcteurs d'erreurs (Théorie de l'information)

Page: 330

View: 883

Codes, Kodierung (Telegrafie) ; Kodierung, Datendarstellung, Bit, Byte (EDV).
Categories: Codes correcteurs d'erreurs (Théorie de l'information)