A Complexity Reducing Transformation for the Lee-O'Sullivan Interpolation Algorithm
Jun Ma, Alexander Vardy · 2007
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.