Deterministic Capacity of MIMO Relay Networks

The deterministic capacity of a relay network is the capacity of a network when relays are restricted to transmitting \emph{reliable} information, that is, (asymptotically) deterministic function of the source message. In this paper it is shown that the deterministic capacity of a number of MIMO relay networks can be found in the low power regime where $\SNR\to0$. This is accomplished through deriving single letter upper bounds and finding the limit of these as $\SNR\to0$. The advantage of this technique is that it overcomes the difficulty of finding optimum distributions for mutual information.