Retrieving Reed-Solomon coded data under interpolation-based list decoding

TL;DR

This paper introduces a transform that allows efficient retrieval of Reed-Solomon coded data using interpolation-based list decoding, reducing computational complexity after an initial setup.

Contribution

It presents a novel transform matrix that enables generator-matrix-based RS data recovery under list decoding with minimal repeated computation.

Findings

Transform matrix computed once for efficiency

Transformation requires $k^{2}$ field multiplications

Enables effective list decoding of RS codes

Abstract

A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from the output list to the desired RS coded data block incurs $k^{2}$ field multiplications, given a code of dimension $k$.