Deterministic Capacity of Networks

In this paper we define the deterministic capacity of a network. The deterministic capacity is defined by restricting nodes to transmitting (asymptotically) deterministic functions of the messages in the network. It can be seen as an upper bound on the set of rates achieved by all possible decode- forward coding schemes, in an abstract sense. A key advantage of the deterministic capacity is that it can be found for a large class of networks, as opposed to the general Shannon capacity of networks, which is generally unknown, even for the relay channel. We derive the deterministic capacity of some MIMO relay channels in the low power regime.