Código Reed–Solomon

Este artigo ou secção contém uma lista de referências no fim do texto, mas as suas fontes não são claras porque não são citadas no corpo do artigo, o que compromete a confiabilidade das informações. Ajude a melhorar este artigo inserindo citações no corpo do artigo. (Outubro de 2012)

Em teoria, a codificação códigos de Reed-Solomon (RS), é um grupo de códigos cíclicos de correção de erros não binários, [1] inventados por Irving S. Reed e Gustave Solomon. Os Códigos RS constituem uma sub-classe de uma ampla classe de códigos cíclicos denominada de Códigos BCH (Bose–Chaudhuri–Hocquenghem). Eles descreveram uma forma sistemática de construção de códigos capazes de detectar e corrigir vários erros aleatórios de símbolos. Ao adicionar $t$ símbolos de verificação aos dados, um código RS pode detectar qualquer combinação de até $t$ símbolos errados, e corrigir até $t/2$ símbolos. Como erasure code consegue corrigir até $t$ faltas conhecidas, ou pode detectar e corrigir uma combinação de erros e faltas. Além disso, os códigos RS são adequados como códigos de correção de multiple-burst bit-error, uma vez que uma sequência de $b+1$ erros consecutivos afeta no máximo dois símbolos de tamanho $b$ . [2] A escolha de $t$ é arbitrária sendo efectuada pelo criador do código, e podendo ser seleccionado dentro de limites amplos.

Os Códigos RS encontram-se entre os códigos mais poderosos no que diz respeito à capacidade de correção de erro, sendo largamente utilizados em muitos sistemas digitais tais como: Comunicações de missões espaciais, CDs, DVDs, aDSL, WiMAX, DVB, QRCode, sistemas RAID 6 e sistemas de telecomunicações como DWDM.

Referências

Cipra, Barry A. (1993), «The Ubiquitous Reed–Solomon Codes», SIAM News, 26 (1)
Berlekamp, Elwyn R. (1967), Nonbinary BCH decoding, International Symposium on Information Theory, San Remo, Italy
Berlekamp, Elwyn R. (1984) [1968], Algebraic Coding Theory, ISBN 0-89412-063-8 Revised ed. , Laguna Hills, CA: Aegean Park Press
Forney, Jr., G. (outubro de 1965), «On Decoding BCH Codes», IEEE Transactions on Information Theory, 11 (4): 549–557, doi:10.1109/TIT.1965.1053825
Gill, John (n.d.), EE387 Notes #7, Handout #28 (PDF), Stanford University, consultado em 21 de abril de 2010
Hong, Jonathan; Vetterli, Martin (agosto de 1995), «Simple Algorithms for BCH Decoding», IEEE Transactions on Communications, 43 (8): 2324–2333
Koetter, Ralf (2005), Reed–Solomon Codes, MIT Lecture Notes 6.451 (Video) ^{[ligação inativa]}
Lin, Shu; Costello, Jr., Daniel J. (1983), Error Control Coding: Fundamentals and Applications, ISBN 0-13-283796-X, New Jersey, NJ: Prentice-Hall
MacWilliams, F. J.; Sloane, N. J. A. (1977), The Theory of Error-Correcting Codes, New York, NY: North-Holland Publishing Company
Massey, J. L. (1969), «Shift-register synthesis and BCH decoding» (PDF), IEEE Transactions on Information Theory, IT-15 (1): 122–127
Peterson, Wesley W. (1960), «Encoding and Error Correction Procedures for the Bose-Chaudhuri Codes», Institute of Radio Engineers, IRE Transactions on Information Theory, IT–6: 459–470
Reed, Irving S.; Chen, Xuemin (1999), Error-Control Coding for Data Networks, Boston, MA: Kluwer Academic Publishers
Reed, Irving S.; Solomon, Gustave (1960), «Polynomial Codes over Certain Finite Fields», Journal of the Society for Industrial and Applied Mathematics (SIAM), 8 (2): 300–304, doi:10.1137/0108018
Welch, L. R. (1997), The Original View of Reed–Solomon Codes (PDF), Lecture Notes

Ligações externas

Schifra Open Source C++ Reed–Solomon Codec
Henry Minsky's RSCode library, Reed–Solomon encoder/decoder
Open source Verilog Reed-Solomon IP
A Tutorial on Reed–Solomon Coding for Fault-Tolerance in RAID-like Systems
Algebraic soft-decoding of Reed–Solomon codes
Matlab implementation of errors and-erasures Reed–Solomon decoding
Pure-Python implementation of a Reed-Solomon codec
BBC R&D White Paper WHP031
Geisel, William A. (agosto de 1990), Tutorial on Reed–Solomon Error Correction Coding (PDF), Technical Memorandum, NASA, TM-102162

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