Asymptotic Interference Alignment for Optimal Repair of MDS Codes in Distributed Storage

The high repair bandwidth cost of (
n
,
k
) maximum distance separable (MDS) erasure codes has motivated a new class of codes that can reduce repair bandwidth over that of conventional MDS codes. In this paper, we address (
n
,
k
,
d
) exact repair MDS codes, which allow for any single failed node to be repaired exactly with access to any arbitrary set of
d
survivor nodes. We show the existence of exact repair MDS codes that achieve minimum repair bandwidth (matching the cut-set lower bound) for arbitrary admissible (
n
,
k
,
d
), i.e.,
k
≤
d
≤
n
-1. Moreover, we extend our results to show the optimality of our codes for multiple-node failure scenarios in which an arbitrary set of
r
≤
n
-
k
failed nodes needs to repaired. Our approach is based on asymptotic interference alignment proposed by Cadambe and Jafar. As a byproduct, we also characterize the capacity of a class of multisource nonmulticast networks.