Optimal locally repairable codes and connections to matroid theory

Itzhak Tamo, Dimitris S. Papailiopoulos, Alexandros G. Dimakis

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly suboptimal for distributed environments due to their high overhead in single-failure events. Locally Repairable Codes (LRCs) form a new family of codes that are repair efficient. In particular, LRCs minimize the number of nodes participating in single node repairs during which they generate small network traffic. Two large-scale distributed storage systems have already implemented different types of LRCs: Windows Azure Storage and the Hadoop Distributed File System RAID used by Facebook. The fundamental bounds for LRCs, namely the best possible distance for a given code locality, were recently discovered, but few explicit constructions exist. In this work, we present an explicit and simple to implement construction of optimal LRCs, for code parameters previously established by existence results. For the analysis of the optimality of our code, we derive a new result on the matroid represented by the code's generator matrix.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages1814-1818
Number of pages5
DOIs
StatePublished - 2013
Externally publishedYes
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/TerritoryTurkey
CityIstanbul
Period7/07/1312/07/13

Funding

FundersFunder number
Directorate for Computer and Information Science and Engineering1217894

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