Efficient Interpolation and Factorization in Algebraic Soft-Decision Decoding of Reed-Solomon Codes

Algebraic soft-decision decoding of Reed-Solomon codes delivers promising coding gains over conventional hard-decision decoding. The main computational steps in algebraic soft-decoding (as well as Sudan-type list-decoding) are bivariate interpolation and factorization. We discuss a new computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the complexity these steps. The re-encoding procedure and the coordinate transformation convert the original interpolation problem into another reduced interpolation problem, which is orders of magnitude smaller than the original one. We present a rigorous proof that the two interpolation problems are equivalent. We also present an efficient factorization procedure that applies directly to the reduced interpolation problem.