  In this paper, we study the capacity of the two-user multiple-input
multiple-output (MIMO) linear deterministic interference channel (IC), with
possible correlations within/between the channel matrices. The capacity region
is characterized in terms of the rank of the channel matrices. It is shown that
\emph{linear precoding} with Han-Kobayashi type of rate-splitting, i.e.,
splitting the information-bearing symbols of each user into common and private
parts, is sufficient to achieve all the rate pairs in the derived capacity
region. The capacity result is applied to obtain an achievable rate region for
the double-unicast networks with random network coding at the intermediate
nodes, which can be modeled by the two-user MIMO linear deterministic IC
studied. It is shown that the newly proposed achievable region is strictly
larger than the existing regions in the literature.
