Quasi-cyclic Regenerating Codes. (arXiv:1209.3977v1 [cs.IT])

from cs.IT updates on arXiv.org http://arxiv.org/abs/1209.3977

In a distributed storage environment, where the data is placed in nodes
connected through a network, it is likely that one of these nodes fails. It is
known that the use of erasure coding improves the fault tolerance and minimizes
the redundancy added in distributed storage environments. The use of
regenerating codes [1] not only make the most of the erasure coding
improvements, but also minimizes the amount of data needed to regenerate a
failed node. In this paper, a new family of regenerating codes based on
quasi-cyclic codes is presented. Quasi-cyclic minimum storage regenerating
(quasi-cyclic MSR) codes are presented and their existence with high
probability is proved. Regenerating codes with optimal bandwidth constructed
from a base MSR code by using graphs are also provided. These codes not only
achieve optimal MBR parameters in terms of stored data and bandwidth, but also
for a specific choice of the parameters involved, they can be decreased under
the optimal MBR point. Quasi-cyclic regenerating codes are also very
interesting be- cause of their simplicity and low complexity. They allow a
repair- by-transfer in the optimal bandwidth case (no operations are needed)
and a pseudo repair-by-transfer in the MSR case, where operations are needed
only when the new node enters into the system replacing a lost one.

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