Optimal Locally Repairable Codes and Connections to Matroid Theory. (arXiv:1301.7693v1 [cs.IT])

from cs.IT updates on arXiv.org http://arxiv.org/abs/1301.7693

Petabyte-scale distributed storage systems are currently transitioning to
erasure codes to achieve higher storage efficiency. Classical codes like
Reed-Solomon are highly sub-optimal for distributed environments due to their
high overhead in single-failure events. {\it 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 while
generating small network traffic for repairs. 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 only by existence
results. % Our construction is very simple to implement. For the analysis of
the code’s optimality, we derive a new result on the matroid represented by the
code’s generator matrix.

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