A Link between Guruswami--Sudan's List--Decoding and Decoding of Interleaved Reed--Solomon Codes

TL;DR

This paper establishes a connection between Welch--Berlekamp decoding for Reed--Solomon codes and Guruswami--Sudan list--decoding, showing that interleaved RS code decoding can be viewed as a modified Guruswami--Sudan problem with similar solution spaces.

Contribution

It introduces a novel formulation linking Welch--Berlekamp decoding of interleaved RS codes to Guruswami--Sudan list--decoding, revealing their equivalence in solution space.

Findings

Decoding of interleaved RS codes can be expressed as a modified Guruswami--Sudan problem.

The new approach yields the same solution space as the Welch--Berlekamp scheme.

Key properties of the connection are proven.

Abstract

The Welch--Berlekamp approach for Reed--Solomon (RS) codes forms a bridge between classical syndrome--based decoding algorithms and interpolation--based list--decoding procedures for list size l=1. It returns the univariate error--locator polynomial and the evaluation polynomial of the RS code as a y-root. In this paper, we show the connection between the Welch--Berlekamp approach for a specific Interleaved Reed--Solomon code scheme and the Guruswami--Sudan principle. It turns out that the decoding of Interleaved RS codes can be formulated as a modified Guruswami--Sudan problem with a specific multiplicity assignment. We show that our new approach results in the same solution space as the Welch--Berlekamp scheme. Furthermore, we prove some important properties.