A link between Guruswami-Sudan's list-decoding and decoding of interleaved Reed-Solomon codes

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.