Exact-Repair MDS Code Construction Using Interference Alignment

The high repair cost of
$(n,k)$
Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of MDS codes, called Repair MDS codes, that can significantly reduce repair bandwidth over conventional MDS codes. In this paper, we describe
$(n,k,d)$
Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to
$d$
survivor nodes, where
$k\leq d\leq n-1$
. We construct Exact-Repair MDS codes that are optimal in repair bandwidth for the cases of:
$(a)~k/n\leq 1/2$
and
$d\geq 2k-1$

In this paper, we assume that all of the survivor systematic nodes participate in the repair.
;
$(b)~k\leq 3$
. Our codes are deterministic and require a finite-field size of at most
$2(n-k)$
. Our constructive codes are based on interference alignment techniques.