  The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes
has recently motivated a new class of codes, called Regenerating Codes, that
optimally trade off storage cost for repair bandwidth. In this paper, we
address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any
failed node to be repaired exactly with access to arbitrary d survivor nodes,
where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve
minimum repair bandwidth (matching the cutset lower bound) for arbitrary
admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on
interference alignment techniques and uses vector linear codes which allow to
split symbols into arbitrarily small subsymbols.
