Prefactor Reduction of the Guruswami–Sudan Interpolation Step

Abstract

The most computationally intensive step of the Guruswami–Sudan list decoder for generalized Reed–Solomon codes is the formation of a bivariate interpolation polynomial. Complexity can be reduced if this polynomial has prefactors, i.e., factors of its univariate constituent polynomials that are independent of the received vector, and hence known a priori . For example, the well-known re-encoding projection due to Koetter et al. leads to one class of prefactors. This paper introduces so-called Sierpinski prefactors that result from the property that many binomial coefficients, which arise in the multiplicity constraints defined in terms of the Hasse derivative, are zero modulo the underlying field characteristic. It is shown that re-encoding prefactors and Sierpinski prefactors can be combined to achieve a significantly reduced Guruswami–Sudan interpolation step. In certain practically relevant cases, the introduction of Sierpinski prefactors reduces the number of unknown polynomial coefficients by an additional 10% or more (beyond the reduction due to re-encoding prefactors alone), without incurring additional computational effort at the decoder.