Message Transmission and Common Randomness Generation Over MIMO Slow Fading Channels With Arbitrary Channel State Distribution

We investigate the problem of message transmission and the problem of common randomness (CR) generation over single-user multiple-input multiple-output (MIMO) slow fading channels with average input power constraint, additive white Gaussian noise (AWGN), arbitrary state distribution and with complete channel state information available at the receiver side (CSIR). We derive a lower and an upper bound on the outage transmission capacity of MIMO slow fading channels for arbitrary state distribution and show that the bounds coincide except possibly at points of discontinuity of the outage transmission capacity, of which there are, at most, countably many. Such discontinuity issues might occur because the channel state distribution is arbitrary. We also establish the capacity of a specific compound MIMO Gaussian channel in order to prove the lower bound on the outage transmission capacity. Furthermore, we define the outage CR capacity for a two-source model with unidirectional communication over a MIMO slow fading channel with arbitrary state distribution and establish a lower and an upper bound on it using our bounds on the outage transmission capacity of the MIMO slow fading channel.