Polynomial evaluator for use in a Reed-Solomon decoder

Details Polynomial evaluator for use in a Reed-Solomon decoder Polynomial evaluator for use in a Reed-Solomon decoder

1996-11-25

1999-10-26

Elmore, Reba I.

Excavating

371 374, 371 377, 371 403, 371 35, 371 378, H03M 1300

Patent

active

059716070

ABSTRACT:
An apparatus, for use in a Reed-Solomon decoder, evaluates a polynomial P(X) iteratively, by substituting .alpha..sup.-(N-j) for X in a jth iteration, to thereby provide a jth evaluation result P(.alpha..sup.-(N-j)), wherein j is an integer ranging from 1 to N, N being a predetermined positive integer, and .alpha. is a primitive element in a finite field GF(2.sup.m). The apparatus comprises: a FIFO buffer having T registers, T being a predefined positive integer; a root input block for sequentially providing a first group of T elements in the finite field during the jth iteration; a multiplier for sequentially multiplying the contents of the FIFO buffer with the first group of T elements in the finite field provided from the root input block, to thereby provide a jth set of T evaluating terms during the jth iteration; a multiplexor for providing T initial evaluating terms to the FIFO buffer during an initialization and providing the jth set of T evaluating terms to the FIFO buffer during the jth iteration, to be stored therein; an addition block for determining a sum of the T evaluating terms of the jth set, to thereby provide a jth sum; and an output block for adding a 0th coefficient of the polynomial to the jth sum, to thereby provide the jth evaluation result during the jth iteration.

REFERENCES:
patent: 4162480 (1979-07-01), Berlekamp
patent: 4649541 (1987-03-01), Lahmeyer
patent: 4958348 (1990-09-01), Berlekamp et al.
patent: 5323402 (1994-06-01), Vaccaro et al.
patent: 5644695 (1997-07-01), Blaum et al.
G.C. Clark, Jr. and J. Bibb Cain, "Error-Correction Coding for Digital Communications" Plenum Press, New York and London, 1981, pp. 188-pp. 195.
R.T. Chien, "Cyclic Decoding Procedures for Bose-Chaudhuri-Hocquenghem Codes" IEEE Transactions on Information Theory, vol. 10, 1964, pp. 357-pp. 363.

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