Polynomial Theory of Error Correcting Codes PDF Download
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Author: Giovanni Cancellieri
Publisher: Springer
ISBN: 3319017276
Category : Technology & Engineering
Languages : en
Pages : 732
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Book Description
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.
Author: Giovanni Cancellieri
Publisher: Springer
ISBN: 3319017276
Category : Technology & Engineering
Languages : en
Pages : 732
Get Book
Book Description
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.
Author: Florence Jessie MacWilliams
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 794
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Book Description
Author: D J. Baylis
Publisher: Routledge
ISBN: 1351449842
Category : Mathematics
Languages : en
Pages : 232
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Book Description
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.
Author: Vera Pless
Publisher: Wiley-Interscience
ISBN:
Category : Computers
Languages : en
Pages : 232
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Book Description
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: Jiri Adamek
Publisher: John Wiley & Sons
ISBN: 1118031512
Category : Computers
Languages : en
Pages : 352
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Book Description
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.
Author: D J. Baylis
Publisher: Routledge
ISBN: 1351449834
Category : Mathematics
Languages : en
Pages : 113
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Book Description
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.
Author: Jaques Calmet
Publisher: Springer Science & Business Media
ISBN: 9783540167761
Category : Computers
Languages : en
Pages : 430
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Book Description
Author: Vera Pless
Publisher: John Wiley & Sons
ISBN: 1118030990
Category : Mathematics
Languages : en
Pages : 226
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Book Description
A complete introduction to the many mathematical tools used to solve practical problems in coding. Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to solve applied problems. Introduction to the Theory of Error-Correcting Codes, Third Edition demonstrates this process and prepares students to cope with coding problems. Like its predecessor, which was awarded a three-star rating by the Mathematical Association of America, this updated and expanded edition gives readers a firm grasp of the timeless fundamentals of coding as well as the latest theoretical advances. This new edition features: * A greater emphasis on nonlinear binary codes * An exciting new discussion on the relationship between codes and combinatorial games * Updated and expanded sections on the Vashamov-Gilbert bound, van Lint-Wilson bound, BCH codes, and Reed-Muller codes * Expanded and updated problem sets. Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.
Author: Florence Jessie MacWilliams
Publisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 762
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Book Description
Author: William Wesley Peterson
Publisher: MIT Press
ISBN: 9780262160391
Category : Computers
Languages : en
Pages : 584
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Book Description
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.
