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In this paper, we study the capacity of the two-user multiple-inputmultiple-output (MIMO) linear deterministic interference channel (IC), withpossible correlations within/between the channel matrices. The capacity regionis 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 privateparts, is sufficient to achieve all the rate pairs in the derived capacityregion. The capacity result is applied to obtain an achievable rate region forthe double-unicast networks with random network coding at the intermediatenodes, which can be modeled by the two-user MIMO linear deterministic ICstudied. It is shown that the newly proposed achievable region is strictlylarger than the existing regions in the literature.

On the Capacity Region of Two-User Linear Deterministic Interference Channel and Its Application to Multi-Session Network Coding