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The Re-Encoding Transformation in Algebraic List-Decoding of Reed–Solomon Codes

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3 Author(s)
Koetter, R. ; Tech. Univ. Munchen, Munich, Germany ; Jim Ma ; Vardy, A.

The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the complexity of the bivariate interpolation procedure. This re-encoding and coordinate transformation converts the original interpolation problem into another reduced interpolation problem, which is orders of magnitude smaller than the original one. A formal proof is presented to show that the two interpolation problems are indeed equivalent. An efficient factorization procedure that applies directly to the reduced interpolation problem is also given.

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Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 2 )