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About 7,793 papers for “error-correcting codes”

Error‐Correcting Codes

Maurice Bellanger · Digital Signal Processing · 2024

Systems for information processing and transmission constitute a major field of application for signal-processing techniques. Error-detection and correction techniques are also widely used in these systems and, therefore, they coexist and even interact with signal processing in communication equipment. This chapter provides an introduction to some important error-correcting codes from a signal-processing perspective, allowing readers to gain an understanding of these codes and assess their strengths and weaknesses. Reed–Solomon codes exploit predictable signals generated by line errors to identify these errors and subtract them from the received signal so as to recover the transmitted signal. Convolutional coding of a sequence of symbols consists of introducing redundancy into the sequence and correlation between symbols. An approach to cope with error packets consists of cascading the convolutional decoder with an interleaver and a Reed–Solomon decoder. Turbo codes combine recursive filtering, interleaving, and an iterative procedure.

Cited by 3

Error Correcting Codes

Christiane Rousseau, Yvan Saint-Aubin · Springer undergraduate texts in mathematics and technology · 2008

Cited by 19

Error-Correcting Codes

John Baylis · 1998

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.

Cited by 3

Error Correcting Codes

David R. Finston, Patrick J. Morandi · Springer undergraduate texts in mathematics and technology · 2014

Cited by 30

Error-correcting codes

Peter J‎. Cameron · Cambridge University Press eBooks · 1994

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

Cited by 4

Error-correcting codes

J. H. van Lint, Gerard van der Geer · Birkhäuser Basel eBooks · 1988

We shall not go into details concerning all the technical applications of error-correcting codes. These include satellite pictures, telephone messages via glass fibre using light, compact disc audio system. The idea is as follows. We consider “information” presented as a very long sequence of symbols from a finite set called the “alphabet”. In this course the alphabet will be a finite field IF q . In the sequence each symbol occurs with equal probability. This information is sent to a receiver over a so-called “noisy channel”. In the model that we consider there is a fixed (small) probability p e that a symbol, that is sent over the channel, is changed into one of the other symbols (again, all equally likely). Such an event is called a “symbol-error” and p e is the symbol-error probability. As a result a fraction p e of the transmitted symbols arrives incorrectly at the receiver end of the channel. The aim of coding theory is to lower the probability of error (considerably) at the expense of spending some of the transmission time or energy on redundant symbols. The idea is explained in one sentence as follows. When we read printed text we recognize a printing error in a word because in our vocabulary there is only one word that resembles (is “sufficiently close to”) the printed word.

Cited by 20