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Fast parallel algorithms for decoding Reed-Solomon codes based on remainder polynomials

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2 Author(s)
Dabiri, D. ; Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada ; Blake, I.F.

The problem of decoding cyclic error correcting codes is one of solving a constrained polynomial congruence, often achieved using the Berlekamp-Massey or the extended Euclidean algorithm on a key equation involving the syndrome polynomial. A module-theoretic approach to the solution of polynomial congruences is developed here using the notion of exact sequences. This technique is applied to the Welch-Berlekamp (1986) key equation for decoding Reed-Solomon codes for which the computation of syndromes is not required. It leads directly to new and efficient parallel decoding algorithms that can be realized with a systolic array. The architectural issues for one of these parallel decoding algorithms are examined in some detail

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 4 )