Guruswami--Sudan List Decoding for Complex Reed--Solomon Codes [article]

Mostafa H. Mohamed and Sven Puchinger and Martin Bossert
2016 arXiv   pre-print
We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing. We propose methods of stabilizing both the interpolation and the root-finding steps against numerical instabilities, where the latter is the most sensitive. For this purpose, we modify the Roth--Ruckenstein algorithm and propose a method to refine its result using Newton's method. The overall decoding performance is then further improved using
more » ... zed Minimum Distance decoding based on intrinsic soft information. This method also allows to obtain a unique solution of the recovery problem. The approach is numerically evaluated and shown to improve upon recently proposed decoding techniques.
arXiv:1611.07811v1 fatcat:zqmnlrqzebafnobbnfdwhqwkfy