  The performance of integer-forcing equalization for communication over the
compound multiple-input multipleoutput channel is investigated. An upper bound
on the resulting outage probability as a function of the gap to capacity has
been derived previously, assuming a random precoding matrix drawn from the
circular unitary ensemble is applied prior to transmission. In the present work
a simple and explicit lower bound on the worst-case outage probability is
derived for the case of a system with two transmit antennas and two or more
receive antennas, leveraging the properties of the Jacobi ensemble. The derived
lower bound is also extended to random space-time precoding, and may serve as a
useful benchmark for assessing the relative merits of various algebraic
space-time precoding schemes. We further show that the lower bound may be
adapted to the case of a $1 \times N_t$ system. As an application of this, we
derive closed-form bounds for the symmetric-rate capacity of the Rayleigh
fading multiple-access channel where all terminals are equipped with a single
antenna. Lastly, we demonstrate that the integer-forcing equalization coupled
with distributed space-time coding is able to approach these bounds.
