Erasure coding techniques are used to increase the reliability of distributed
storage systems while minimizing storage overhead. Also of interest is
minimization of the bandwidth required to repair the system following a node
failure. In a recent paper, Wu et al. characterize the tradeoff between the
repair bandwidth and the amount of data stored per node. They also prove the
existence of regenerating codes that achieve this tradeoff.
In this paper, we introduce Exact Regenerating Codes, which are regenerating
codes possessing the additional property of being able to duplicate the data
stored at a failed node. Such codes require low processing and communication
overheads, making the system practical and easy to maintain. Explicit
construction of exact regenerating codes is provided for the minimum bandwidth
point on the storage-repair bandwidth tradeoff, relevant to
distributed-mail-server applications. A subspace based approach is provided and
shown to yield necessary and sufficient conditions on a linear code to possess
the exact regeneration property as well as prove the uniqueness of our
construction.
Also included in the paper, is an explicit construction of regenerating codes
for the minimum storage point for parameters relevant to storage in
peer-to-peer systems. This construction supports a variable number of nodes and
can handle multiple, simultaneous node failures. All constructions given in the
paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on
Communication, Control and Computing, September 200
