  We present a deterministic channel model which captures several key features
of multiuser wireless communication. We consider a model for a wireless network
with nodes connected by such deterministic channels, and present an exact
characterization of the end-to-end capacity when there is a single source and a
single destination and an arbitrary number of relay nodes. This result is a
natural generalization of the max-flow min-cut theorem for wireline networks.
Finally to demonstrate the connections between deterministic model and Gaussian
model, we look at two examples: the single-relay channel and the diamond
network. We show that in each of these two examples, the capacity-achieving
scheme in the corresponding deterministic model naturally suggests a scheme in
the Gaussian model that is within 1 bit and 2 bit respectively from cut-set
upper bound, for all values of the channel gains. This is the first part of a
two-part paper; the sequel [1] will focus on the proof of the max-flow min-cut
theorem of a class of deterministic networks of which our model is a special
case.
