  The sum degrees of freedom (DoF) of the two-transmitter, two-receiver
multiple-input multiple-output (MIMO) X-Network ($2 \times 2$ MIMO X-Network)
with $M$ antennas at each node is known to be $\frac{4M}{3}$. Transmission
schemes which couple local channel-state-information-at-the-transmitter (CSIT)
based precoding with space-time block coding to achieve the sum-DoF of this
network are known specifically for $M=2,4$. These schemes have been proven to
guarantee a diversity gain of $M$ when a finite-sized input constellation is
employed. In this paper, an explicit transmission scheme that achieves the
$\frac{4M}{3}$ sum-DoF of the $2 \times 2$ X-Network for arbitrary $M$ is
presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai
scheme which requires the availability of global CSIT in order to achieve the
$\frac{4M}{3}$ sum-DoF. Further, it is shown analytically that the proposed
scheme guarantees a diversity gain of $M+1$ when finite-sized input
constellations are employed.
