Re-Encoding Techniques for Interpolation-Based Decoding of Reed-Solomon Codes

We consider interpolation-based decoding of Reed-Solomon codes using the Guruswami-Sudan algorithm (GSA) and investigate the effects of two modification techniques for received vectors, i.e., the re-encoding map and the newly introduced periodicity projection. After an analysis of the latter, we track the benefits (that is low Hamming weight and regular structure) of modified received vectors through the interpolation step of the GSA and show how the involved homogeneous linear system of equations can be compressed. We show that this compression as well as the recovery of the interpolated bivariate polynomial is particularly simple when the periodicity projection was applied.