Behavioral Models for List Decoding

Abstract

Recently it has been shown that list decoding of Reed-Solomon codes may be translated into a bivariate interpolation problem. The data consist of pairs in a finite field and the aim is to find a bivariate polynomial that interpolates the given pairs and is minimal with respect to some criterion. We present a systems theoretic approach to this interpolation problem. With the data points we associate a set of time series, also called trajectories. For this set of trajectories we construct the Most Powerful Unfalsified Model (MPUM). This is the smallest possible model that explains these trajectories. The bivariate polynomial is then derived from a specific polynomial representation of the MPUM.