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

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

2010-06-08

arxiv.org/abs/1006.1658v1

Computer Science

Information Theory

For ISIT 2010

Scientific paper

10.1109/ISIT.2010.5513427

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.

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