A Link between Guruswami--Sudan's List--Decoding and Decoding of
Interleaved Reed--Solomon Codes
release_sjwjdyqt45eoxpea5h5agign34
by
Alexander Zeh, Christian Senger
2010
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.
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1006.1658v1
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