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

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3 Author(s)
Ralf Koetter ; Technische Universität München, Munich, Germany ; Jun Ma ; Alexander Vardy

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.

Published in:

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