Power Decoding of Reed-Solomon Codes Revisited

TL;DR

This paper introduces a new variant of Power decoding for Reed-Solomon codes based on Gao's key equation, providing insights into its properties and failure bounds beyond traditional decoding limits.

Contribution

A novel Power decoding variant for Reed-Solomon codes utilizing Gao's key equation, with analysis of its behavior and failure probability.

Findings

Behavioral equivalence to classical syndrome-based decoding

New failure probability bound for powering degree 3

Enhanced understanding of decoding beyond half the minimum distance

Abstract

Power decoding, or "decoding by virtual interleaving", of Reed--Solomon codes is a method for unique decoding beyond half the minimum distance. We give a new variant of the Power decoding scheme, building upon the key equation of Gao. We show various interesting properties such as behavioural equivalence to the classical scheme using syndromes, as well as a new bound on the failure probability when the powering degree is 3.