A Complexity Reducing Transformation for the Lee-O´Sullivan Interpolation Algorithm

Recently, Lee and O´Sullivan proposed a new interpolation algorithm for algebraic soft-decision decoding of Reed- Solomon codes. In some cases, the Lee-O´Sullivan algorithm turns out to be substantially more efficient than alternative interpolation approaches, such as Koetter´s algorithm. Herein, we combine the re-encoding coordinate transformation, originally developed in the context of Koetter´s algorithm, with the recent interpolation technique of Lee and O´Sullivan. To this end, we develop a new basis construction algorithm, which takes into account the additional constraints imposed by the reduced interpolation problem that results upon the re-encoding transformation. This reduces the computational and storage complexity of the Lee-O´Sullivan algorithm by orders of magnitude, and makes it directly comparable to Koetter´s algorithm in situations of practical importance.