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
Category: Technology & Engineering
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.
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
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.
But from the proof of Theorem 6.1 this n is precisely the maximal number of
columns of length n - / with no pair of columns dependent. Hence, by definition С
is a Hamming code. Moving on to 2-error correcting linear codes, the condition
Author: D J. Baylis
Publisher: CRC Press
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.
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
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.
We have gathered linear codes in classes of codes which are of the same quality
with respect to error correction. Since the metric structure of a code determines its error correction properties we have introduced the notion of isometric codes ...
Author: Anton Betten
Publisher: Springer Science & Business Media
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.
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.
This book provides and elementary, yet rigorous, introduction to the theory of error-correcting codes.
Author: Raymond Hill
Publisher: Oxford University Press
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.
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.
Author: Torleiv Klove
Publisher: World Scientific
Category: Computer science
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.
This book is open access under a CC BY 4.0 license. This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes.
Author: Martin Tomlinson
Category: Technology & Engineering
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.
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 ...
Author: Benjamin Arazi
Publisher: MIT Press
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.
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
Category: Computer programming
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.
This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999.
Author: Marc Fossorier
This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.
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.
Author: Venkatesan GuruswamiPublish On: 2004-11-29
This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”.
Author: Venkatesan Guruswami
How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the 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 errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.