Efficient List-Decoding of Reed-Solomon Codes with the Fundamental Iterative Algorithm

Alexander Zeh (1, 2) , Christian Gentner (3) , Martin Bossert (2)

1 TANC - Algorithmic number theory for cryptology
2 INT - University of Ulm. - Institute of Communications Engineering [Ulm]
3 DLR - German Aerospace Center

In this paper we propose a new algorithm that solves the Guruswami-Sudan interpolation step for Reed-Solomon codes efficiently. It is a generalization of the Feng-Tzeng approach, the so-called fundamental iterative algorithm. From the interpolation constraints of the Guruswami-Sudan principle it is well known that an improvement of the decoding radius can only be achieved, if the multiplicity parameter s is smaller than the list size l. The code length is n and our proposed algorithm has a complexity (without asymptotic assumptions) of O(ls4 n2).}, keywords={Feng-Tzeng approach;Guruswami-Sudan interpolation;Reed-Solomon codes;communication complexity;efficient list-decoding;fundamental iterative algorithm;Reed-Solomon codes;communication complexity;decoding;iterative methods;

Mots clés: codescommunication; complexity; efficient; feng-tzeng; fundamental; guruswami-sudan; list-decoding; reed-solomon

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Alexander Zeh, Christian Gentner, Martin Bossert. Efficient List-Decoding of Reed-Solomon Codes with the Fundamental Iterative Algorithm. IEEE Information Theory Workshop (ITW), Sep 2010, Taorminia, Italy. pp.130-134, ⟨10.1109/ITW.2009.5351241⟩. ⟨hal-00647592⟩