Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding

TL;DR

This paper introduces an improved partial decoding algorithm for interleaved Reed-Solomon codes that enhances decoding capability at high error rates across all code rates, combining collaborative and power decoding techniques.

Contribution

It presents a novel partial decoding algorithm for IRS codes that outperforms previous methods for rates above 1/3, using a combination of collaborative and power decoding.

Findings

Decodes errors with relative weight up to 1 - R^{m/(m+1)} with high probability.

Achieves polynomial time decoding for all code rates.

First significant improvement for rates above 1/3 in two decades.

Abstract

We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code length $n$. For $m>2$, this is an asymptotic improvement over the previous state-of-the-art for all rates, and the first improvement for $R>1/3$ in the last $20$ years. The method combines collaborative decoding of IRS codes with power decoding up to the Johnson radius.