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Abstract: The main computational steps in algebraic soft-decoding, as well asSudan-type list-decoding, of Reed-Solomon codes are bivariate polynomialinterpolation and factorization. We introduce a computational technique, basedupon re-encoding and coordinate transformation, that significantly reduces thecomplexity of the bivariate interpolation procedure. This re-encoding andcoordinate transformation converts the original interpolation problem intoanother reduced interpolation problem, which is orders of magnitude smallerthan the original one. A rigorous proof is presented to show that the twointerpolation problems are indeed equivalent. An efficient factorizationprocedure that applies directly to the reduced interpolation problem is alsogiven.



Author: Ralf Koetter, Jun Ma, Alexander Vardy

Source: https://arxiv.org/







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