Polynomial Theory of Error Correcting Codes

Polynomial Theory of Error Correcting Codes PDF

Author: Giovanni Cancellieri

Publisher: Springer

Published: 2014-11-08

Total Pages: 736

ISBN-13: 3319017276

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The book offers an original view on channel coding, based on a unitary approach to block and convolutional codes for error correction. It presents both new concepts and new families of codes. For example, lengthened and modified lengthened cyclic codes are introduced as a bridge towards time-invariant convolutional codes and their extension to time-varying versions. The novel families of codes include turbo codes and low-density parity check (LDPC) codes, the features of which are justified from the structural properties of the component codes. Design procedures for regular LDPC codes are proposed, supported by the presented theory. Quasi-cyclic LDPC codes, in block or convolutional form, represent one of the most original contributions of the book. The use of more than 100 examples allows the reader gradually to gain an understanding of the theory, and the provision of a list of more than 150 definitions, indexed at the end of the book, permits rapid location of sought information.

Introduction to the Theory of Error-correcting Codes

Introduction to the Theory of Error-correcting Codes PDF

Author: Vera Pless

Publisher: Wiley-Interscience

Published: 1989

Total Pages: 232

ISBN-13:

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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.

Error Correcting Codes

Error Correcting Codes PDF

Author: D J. Baylis

Publisher: Routledge

Published: 2018-05-11

Total Pages: 113

ISBN-13: 1351449834

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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.

Foundations of Coding

Foundations of Coding PDF

Author: Jiri Adamek

Publisher: John Wiley & Sons

Published: 2011-02-14

Total Pages: 352

ISBN-13: 1118031512

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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.

Error-correcting Codes

Error-correcting Codes PDF

Author: William Wesley Peterson

Publisher: MIT Press

Published: 1972

Total Pages: 584

ISBN-13: 9780262160391

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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 Correcting Codes

Error Correcting Codes PDF

Author: Alain Poli

Publisher:

Published: 1992

Total Pages: 536

ISBN-13:

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This advanced text covers both the theory and applications of coding theory. Drawing on recent research, the book explains new developments in the field of information coding. Included are worked examples and exercises.

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