A new class of MDS erasure codes based on graphs

Authors:
Nattakan Puttarak;Phisan Kaewprapha;Ng Boon Chong;Jing Li
Affiliations:
Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA;Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA;College of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA
Venue:
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Year:
2009

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Abstract

Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested graphs, termed complete-graph-of-rings (CGR). We discuss a systematic and concrete way to transfer these graphs to array codes, unveil an interesting relation between the proposed map and the renowned perfect 1-factorization, and show that the proposed CGR codes subsume B-codes as their "contracted" codes. These new codes, termed CGR codes, and their dual codes are simple to describe, and require minimal encoding and decoding complexity.