Efficient Interpolation in the Guruswami-Sudan Algorithm

TL;DR

This paper introduces an efficient interpolation algorithm for the Guruswami-Sudan list decoding, leveraging binary exponentiation and re-encoding to improve performance and reduce complexity.

Contribution

It presents a novel randomized ideal multiplication algorithm and extends Lee-O'Sullivan's method for faster interpolation in list decoding.

Findings

Achieves asymptotic performance gains

Demonstrates practical efficiency improvements

Reduces complexity through re-encoding integration

Abstract

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.