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.Comment: Submitted to IEEE Transactions on Information Theor