DocumentCode :
1757200
Title :
A Repair Framework for Scalar MDS Codes
Author :
Shanmugam, Karthikeyan ; Papailiopoulos, Dimitris S. ; Dimakis, Alexandros G. ; Caire, Giuseppe
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA
Volume :
32
Issue :
5
fYear :
2014
fDate :
41760
Firstpage :
998
Lastpage :
1007
Abstract :
Several works have developed vector-linear maximum-distance separable (MDS) storage codes that minimize the total communication cost required to repair a single coded symbol after an erasure, referred to as repair bandwidth (BW). Vector codes allow communicating fewer sub-symbols per node, instead of the entire content. This allows non trivial savings in repair BW. In sharp contrast, classic codes, like Reed-Solomon (RS), used in current storage systems, are deemed to suffer from naive repair, i.e. downloading the entire stored message to repair one failed node. This mainly happens because they are scalar-linear. In this work, we present a simple framework that treats scalar codes as vector-linear. In some cases, this allows significant savings in repair BW. We show that vectorized scalar codes exhibit properties that simplify the design of repair schemes. Our framework can be seen as a finite field analogue of real interference alignment. Using our simplified framework, we design a scheme that we call clique-repair which provably identifies the best linear repair strategy for any scalar 2-parity MDS code, under some conditions on the sub-field chosen for vectorization. We specify optimal repair schemes for specific (5,3)- and (6,4)-Reed-Solomon (RS) codes. Further, we present a repair strategy for the RS code currently deployed in the Facebook Analytics Hadoop cluster that leads to 20% of repair BW savings over naive repair which is the repair scheme currently used for this code.
Keywords :
Reed-Solomon codes; linear codes; (5,3)-Reed-Solomon codes; (6,4)-Reed-Solomon codes; Facebook Analytics Hadoop cluster; RS codes; best linear repair strategy; clique-repair; real interference alignment; repair bandwidth framework; scalar 2-parity MDS code; single coded symbol; storage systems; total communication cost; vector-linear maximum-distance separable storage codes; Bandwidth; Interference; Maintenance engineering; Polynomials; Systematics; Vectors; Reed Solomon; Scalar MDS Codes; alignment; clique-repair;
fLanguage :
English
Journal_Title :
Selected Areas in Communications, IEEE Journal on
Publisher :
ieee
ISSN :
0733-8716
Type :
jour
DOI :
10.1109/JSAC.2014.140519
Filename :
6804944
Link To Document :
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