Efficient Interpolation in the Guruswami-Sudan Algorithm

A novel algorithm is proposed for the interpolation step of the Guruswami-Sudan list decoding algorithm. The proposed method is based on the binary exponentiation algorithm, and can be considered as an extension of the Lee-O'Sullivan algorithm. The algorithm is shown to achieve both asymptotical and practical performance gain compared to the case of iterative interpolation algorithm. Further complexity reduction is achieved by integrating the proposed method with re-encoding. The key contribution of the paper, which enables the complexity reduction, is a novel randomized ideal multiplication algorithm.Comment: Submitted to IEEE Transactions on Information Theor

Prefactor Reduction of the Guruswami-Sudan Interpolation Step

The concept of prefactors is considered in order to decrease the complexity of the Guruswami-Sudan interpolation step for generalized Reed-Solomon codes. It is shown that the well-known re-encoding projection due to Koetter et al. leads to one type of such prefactors. The new type of Sierpinski prefactors is introduced. The latter are based on the fact that many binomial coefficients in the Hasse derivative associated with the Guruswami-Sudan interpolation step are zero modulo the base field characteristic. It is shown that both types of prefactors can be combined and how arbitrary prefactors can be used to derive a reduced Guruswami-Sudan interpolation step.Comment: 13 pages, 3 figure