2 research outputs found
On the Achievability Region of Regenerating Codes for Multiple Erasures
We study the problem of centralized exact repair of multiple failures in
distributed storage. We describe constructions that achieve a new set of
interior points under exact repair. The constructions build upon the layered
code construction by Tian et al., designed for exact repair of single failure.
We firstly improve upon the layered construction for general system parameters.
Then, we extend the improved construction to support the repair of multiple
failures, with varying number of helpers. In particular, we prove the
optimality of one point on the functional repair tradeoff of multiple failures
for some parameters. Finally, considering minimum bandwidth cooperative repair
(MBCR) codes as centralized repair codes, we determine explicitly the best
achievable region obtained by space-sharing among all known points, including
the MBCR point
New constructions of cooperative MSR codes: Reducing node size to
We consider the problem of multiple-node repair in distributed storage
systems under the cooperative model, where the repair bandwidth includes the
amount of data exchanged between any two different storage nodes. Recently,
explicit constructions of MDS codes with optimal cooperative repair bandwidth
for all possible parameters were given by Ye and Barg (IEEE Transactions on
Information Theory, 2019). The node size (or sub-packetization) in this
construction scales as , where is the number of failed
nodes and is the code length.
In this paper, we give new explicit constructions of optimal MDS codes for
all possible parameters under the cooperative model, and the node size of our
new constructions only scales as for any number of failed nodes.
Furthermore, it is known that any optimal MDS code under the cooperative model
(including, in particular, our new code construction) also achieves optimal
repair bandwidth under the centralized model, where the amount of data
exchanged between failed nodes is not included in the repair bandwidth. We
further show that the node size of our new construction is also much smaller
than that of the best known MDS code constructions for the centralized model