The first focus of the present paper, is on lower bounds on the
sub-packetization level α of an MSR code that is capable of carrying out
repair in help-by-transfer fashion (also called optimal-access property). We
prove here a lower bound on α which is shown to be tight for the case
d=(n−1) by comparing with recent code constructions in the literature.
We also extend our results to an [n,k] MDS code over the vector alphabet.
Our objective even here, is on lower bounds on the sub-packetization level
α of an MDS code that can carry out repair of any node in a subset of
w nodes, 1≤w≤(n−1) where each node is repaired (linear repair) by
help-by-transfer with minimum repair bandwidth. We prove a lower bound on
α for the case of d=(n−1). This bound holds for any w(≤n−1) and
is shown to be tight, again by comparing with recent code constructions in the
literature. Also provided, are bounds for the case d<(n−1).
We study the form of a vector MDS code having the property that we can repair
failed nodes belonging to a fixed set of Q nodes with minimum repair
bandwidth and in optimal-access fashion, and which achieve our lower bound on
sub-packetization level α. It turns out interestingly, that such a code
must necessarily have a coupled-layer structure, similar to that of the Ye-Barg
code.Comment: Revised for ISIT 2018 submissio