60,430 research outputs found
Optimal Locally Repairable Codes and Connections to Matroid Theory
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. 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 optimal LRCs that are simple to construct. Our construction is
based on grouping Reed-Solomon (RS) coded symbols to obtain RS coded symbols
over a larger finite field. We then partition these RS symbols in small groups,
and re-encode them using a simple local code that offers low repair locality.
For the analysis of the optimality of the code, we derive a new result on the
matroid represented by the code generator matrix.Comment: Submitted for publication, a shorter version was presented at ISIT
201
Optimal Locally Repairable Codes via Rank-Metric Codes
This paper presents a new explicit construction for locally repairable codes
(LRCs) for distributed storage systems which possess all-symbols locality and
maximal possible minimum distance, or equivalently, can tolerate the maximal
number of node failures. This construction, based on maximum rank distance
(MRD) Gabidulin codes, provides new optimal vector and scalar LRCs. In
addition, the paper also discusses mechanisms by which codes obtained using
this construction can be used to construct LRCs with efficient repair of failed
nodes by combination of LRC with regenerating codes
Improving the Secrecy of Distributed Storage Systems using Interference Alignment
Regenerating codes based on the approach of interference alignment for
wireless interference channel achieve the cut-set bound for distributed storage
systems. These codes provide data reliability, and perform efficient exact node
repair when some node fails. Interference alignment as a concept is especially
important to improve the repair efficiency of a failed node in a minimum
storage regenerating (MSR) code. In addition it can improve the stored data
security in presence of passive intruders. In this paper we construct a new
code resilient against a threat model where a passive eavesdropper can access
the data stored on a subset of nodes and the downloaded data during the repair
process of a subset of failed nodes. We achieve an optimal secrecy capacity for
the new explicit construction of MSR interference alignment code. Hence, we
show that the eavesdropper obtains zero information from the original message
stored across the distributed storage, and that we achieve a perfect secrecy.Comment: 20 pages, 3 figure
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