Exact-MSR Codes for Distributed Storage with Low Repair Complexity. (arXiv:1203.2202v1 [cs.IT])

from cs.IT updates on arXiv.org http://arxiv.org/abs/1203.2202

In this paper, we propose two new constructions of exact-repair minimum
storage regenerating (exact-MSR) codes. For both constructions, the encoded
symbols are obtained by treating the message vector over GF(q) as a linearized
polynomial and evaluating it over an extension field GF(q^m). For our exact-MSR
codes, data repair does not need matrix inversion, and can be implemented by
additions and multiplications over GF$(q)$ as well as cyclic shifts when a
normal basis is used. The two constructions assume a base field of GF(q) (q>2)
and GF(2), respectively. In contrast to existing constructions of exact-MSR
codes, the former construction works for arbitrary code parameters, provided
that $q$ is large enough. This is the first construction of exact-MSR codes
with arbitrary code parameters, to the best of our knowledge. In comparison to
existing exact-MSR codes, while data construction of our exact-MSR codes has a
higher complexity, the complexity of data repair is lower. Thus, they are
attractive for applications that need a small number of data reconstructions
along with a large number of data repairs.

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