  Integer forcing is an equalization scheme for the multiple-input
multiple-output communication channel that has been demonstrated to allow
operating close to capacity for "most" channels. In this work, the measure of
"bad" channels is quantified by considering a compound channel setting where
the transmitter communicates over a fixed channel but knows only its mutual
information. The transmitter encodes the data into independent streams, all
taken from the same linear code. The coded streams are transmitted after
applying a unitary transformation. At the receiver side, integer-forcing
equalization is applied, followed by standard single-stream decoding.
Considering pre-processing matrices drawn from a random ensemble, outage
corresponds to the event that the target rate exceeds the achievable rate of
integer forcing for a given channel matrix. For the case of the circular
unitary ensemble, an explicit universal bound on the outage probability for a
given target rate is derived that holds for any channel in the compound class.
The derived bound depends only on the gap-to-capacity and the number of
transmit antennas. The results are also applied to obtain universal bounds on
the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via
linear pre-processed integer forcing.
