  We study the effects of instantaneous feedback of channel topology on the
degrees of freedom (DoF) of the bursty MIMO X channel, where the four
transmitter-receiver links are intermittently on-and-off, governed by four
independent Bernoulli $(p)$ random sequences, and each transmitter and receiver
are equipped with $M$ and $N$ antennas, respectively. We partially characterize
this channel: The sum DoF is characterized when $p\le \frac{1}{2}$ or when
$\frac{\min(M,N)}{\max(M,N)} \le \frac{2}{3}$. In the remaining regime, the
lower bound is within $5.2\%$ of the upper bound. Strictly higher DoF is
achieved by coding across channel topologies. In particular, codes over as many
as $5$ topologies are proposed to achieve the sum DoF of the channel when $p\le
\frac{1}{2}$. A transfer function view of the network is employed to simplify
the code design and to elucidate the fact that these are space-time codes,
obtained by interference alignment over space and time.
