Error Correcting Codes from Linear Sequential Circuits

Error Correcting Codes from Linear Sequential Circuits PDF Author: Stanford University. Stanford Electronics Laboratories
Publisher:
ISBN:
Category :
Languages : en
Pages : 32

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Error Correcting Codes from Linear Sequential Circuits

Error Correcting Codes from Linear Sequential Circuits PDF Author: Stanford University. Stanford Electronics Laboratories
Publisher:
ISBN:
Category :
Languages : en
Pages : 32

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Book Description


Error-Correcting Linear Codes

Error-Correcting Linear Codes PDF Author: Anton Betten
Publisher: Springer Science & Business Media
ISBN: 3540317031
Category : Mathematics
Languages : en
Pages : 798

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Book Description
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.

Error-correcting Codes

Error-correcting Codes PDF 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.

Linear Network Error Correction Coding

Linear Network Error Correction Coding PDF Author: Xuan Guang
Publisher: Springer Science & Business Media
ISBN: 1493905880
Category : Computers
Languages : en
Pages : 107

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Book Description
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.

Error Correcting Codes

Error Correcting Codes PDF 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.

Fundamentals of Error-Correcting Codes

Fundamentals of Error-Correcting Codes PDF Author: W. Cary Huffman
Publisher: Cambridge University Press
ISBN: 1139439502
Category : Technology & Engineering
Languages : en
Pages : 668

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Book Description
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.

The Theory of Error-Correcting Codes

The Theory of Error-Correcting Codes PDF Author: Florence Jessie MacWilliams
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 794

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List Decoding of Error-Correcting Codes

List Decoding of Error-Correcting Codes PDF Author: Venkatesan Guruswami
Publisher: Springer
ISBN: 3540301801
Category : Computers
Languages : en
Pages : 352

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Book Description
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.

The Theory of Error-correcting Codes

The Theory of Error-correcting Codes PDF Author: Florence Jessie MacWilliams
Publisher: Elsevier
ISBN: 0444850104
Category : Computers
Languages : en
Pages : 787

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A New Class of Nonlinear Error-correcting Codes

A New Class of Nonlinear Error-correcting Codes PDF Author: Stanford University. Stanford Electronics Laboratories
Publisher:
ISBN:
Category : Error-correcting codes (Information theory)
Languages : en
Pages : 74

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