Method and apparatus for decoding Reed-Solomon code

Details Method and apparatus for decoding Reed-Solomon code Method and apparatus for decoding Reed-Solomon code

1992-09-24

1994-08-23

Baker, Stephen M.

Excavating

H03M 1300

Patent

active

053413857

ABSTRACT:
A decoding method of Reed-Solomon code produces an error position polynomial .sigma.(x) and an error evaluation polynomial .omega.(x) by a Euclidean algorithm, whereby a syndrome polynomial S(x) is obtained, the highest degrees of the syndrome polynomial S(x) and of an initial polynomial x.sup.2t, which is determined by the number t of symbols to be corrected, are multiplied, while the degree is incrementally reduced, thereby obtaining polynomials h(x) and g(x) that satisfy the relation:

REFERENCES:
patent: 4649541 (1987-03-01), Lahmeyer
Brent, R., et al., "Systolic VLSI Arrays for Polynomial GCD Computation", IEEE Trans. on Computers, vol. C-33, No. 8, Aug. 1984, pp. 731-736.
Shao, H., et al., "A VLSI Design of a Pipeline Reed-Solomon Decoder", IEEE Trans. on Computers, vol. C-34, No. 5, May 1985, pp. 393-403.
Clark, G. et al., Error-Correction Coding for Digital Communications, copyright 1981, Plenum Press, N.Y., pp. 188-201.
Shao, H., et al., "A Single Chip VLSI Reed-Solomon Decoder", ICASSP 86 Proceedings, International Conference on Acoustic, Speech and Signal Processing (Apr. 7-11, 1986, Tokyo, Japan, pp. 2151-2154).
"A Method for Solving Key Equation For Decoding Goppa Codes", Information and Control, vol. 27, 1975, New York, pp. 87-99.

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