  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. On one end of this
spectrum of Regenerating Codes are Minimum Storage Regenerating (MSR) codes
that can match the minimum storage cost of MDS codes while also significantly
reducing repair bandwidth. In this paper, we describe Exact-MSR codes which
allow for any failed nodes (whether they are systematic or parity nodes) to be
regenerated exactly rather than only functionally or information-equivalently.
We show that Exact-MSR codes come with no loss of optimality with respect to
random-network-coding based MSR codes (matching the cutset-based lower bound on
repair bandwidth) for the cases of: (a) k/n <= 1/2; and (b) k <= 3. Our
constructive approach is based on interference alignment techniques, and,
unlike the previous class of random-network-coding based approaches, we provide
explicit and deterministic coding schemes that require a finite-field size of
at most 2(n-k).
