FNT-based Reed-Solomon erasure codes

Authors:
Alexandre Sora;Jérôme Lacan
Affiliations:
University of Toulouse, ISAE/DMIA, Toulouse, France;University of Toulouse, ISAE/DMIA, Toulouse, France
Venue:
CCNC'10 Proceedings of the 7th IEEE conference on Consumer communications and networking conference
Year:
2010

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Abstract

This paper presents a new construction of Maximum-Distance Separable (MDS) Reed-Solomon erasure codes based on Fermat Number Transform (FNT). Thanks to FNT, these codes support practical coding and decoding algorithms with complexity O(n log n), where n is the number of symbols of a codeword. An open-source implementation shows that the encoding speed can reach 150Mbps for codes of length up to several 10,000s of symbols. These codes can be used as the basic component of the Information Dispersal Algorithm (IDA) system used in a several P2P systems.