A unifying system-theoretic framework for errors-and-erasures reed-solomon decoding

Abstract

In the literature there exist several methods for errors-anderasures decoding of RS codes. In this paper we present a unified approach that makes use of behavioral systems theory. We show how different classes of existing algorithms (e. g., syndrome based or interpolation based, non-iterative, erasure adding or erasure deleting) fit into this framework. In doing this, we introduce a slightly more general WB key equation and show how this allows for the handling of erasure locations in a natural way.