36,591 research outputs found
Distributed Storage Systems based on Equidistant Subspace Codes
Distributed storage systems based on equidistant constant dimension codes are
presented. These equidistant codes are based on the Pl\"{u}cker embedding,
which is essential in the repair and the reconstruction algorithms. These
systems posses several useful properties such as high failure resilience,
minimum bandwidth, low storage, simple algebraic repair and reconstruction
algorithms, good locality, and compatibility with small fields
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
Locally Encodable and Decodable Codes for Distributed Storage Systems
We consider the locality of encoding and decoding operations in distributed
storage systems (DSS), and propose a new class of codes, called locally
encodable and decodable codes (LEDC), that provides a higher degree of
operational locality compared to currently known codes. For a given locality
structure, we derive an upper bound on the global distance and demonstrate the
existence of an optimal LEDC for sufficiently large field size. In addition, we
also construct two families of optimal LEDC for fields with size linear in code
length.Comment: 7 page
Explicit MBR All-Symbol Locality Codes
Node failures are inevitable in distributed storage systems (DSS). To enable
efficient repair when faced with such failures, two main techniques are known:
Regenerating codes, i.e., codes that minimize the total repair bandwidth; and
codes with locality, which minimize the number of nodes participating in the
repair process. This paper focuses on regenerating codes with locality, using
pre-coding based on Gabidulin codes, and presents constructions that utilize
minimum bandwidth regenerating (MBR) local codes. The constructions achieve
maximum resilience (i.e., optimal minimum distance) and have maximum capacity
(i.e., maximum rate). Finally, the same pre-coding mechanism can be combined
with a subclass of fractional-repetition codes to enable maximum resilience and
repair-by-transfer simultaneously
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