Outage Common Randomness Capacity Characterization of Multiple-Antenna Slow Fading Channels

We investigate the problem of common randomness (CR) generation from discrete correlated sources aided by one-way communication over single-user multiple-input multiple-output (MIMO) slow fading channels with additive white Gaussian noise (AWGN), arbitrary state distribution and with channel state information available at the receiver side (CSIR). We completely solve the problem by first characterizing the channel outage capacity of MIMO slow fading channels for arbitrary state distribution. For this purpose, we also provide an achievable rate for a specific compound MIMO Gaussian channel. Second, we define the outage CR capacity of the MIMO slow fading channel and establish a single-letter characterization of it using our result on its outage transmission capacity.