  In this paper, we consider an intensity modulated direct detection MIMO
optical wireless communication (OWC) system. For such a system, a novel
super-rectangular cover theory is developed to characterize both the unique
identifiability and full reliability. This theory states that a transmitted
matrix signal can be uniquely identified if and only if the cover order is
equal to the transmitter aperture number, i.e., full cover. In addition, we
prove that full reliability is guaranteed for space-time block coded MIMO-OWC
over commonly used log-normal fading channels with an ML detector if and only
if the STBC enables full cover. In addition, the diversity gain can be
geometrically interpreted as the cover order of the super-rectangle, which
should be maximized, and the volume of this super-rectangle, as the diversity
loss, should be minimized. Using this established error performance criterion,
the optimal linear STBC for block fading channels is proved to be spatial
repetition code with an optimal power allocation. The design of the optimal
non-linear STBC is shown to be equivalent to constructing the optimal
multi-dimensional constellation. Specifically, a multi-dimensional
constellation from Diophantine equations is proposed and then, shown to be more
energy-efficient than the commonly used nonnegative pulse amplitude modulation
constellation.
