Cut-set bound for generalized networks with deterministic channels

The classical discrete memoryless network (DMN) is characterized by one channel and every node in the network incurs a delay. On the other hand, the generalized DMN can be characterized by multiple channels and some nodes in the network may incur no delay. It is well-known that the classical cut-set bound serves as an outer bound for the classical DMN, but it is not applicable to some generalized DMNs. In this paper, we investigate the generalized DMN consisting of only deterministic channels, which we call the generalized deterministic DMN. We show that the capacity region of the generalized deterministic DMN is contained in the classical cut-set outer bound. Using the cut-set bound and the existing rate region achievable by noisy network coding, we are able to derive the capacity regions for some generalized deterministic DMNs under the multimessage multicast scenario.