  The framework of network equivalence theory developed by Koetter et al.
introduces a notion of channel emulation to construct noiseless networks as
upper (resp. lower) bounding models, which can be used to calculate the outer
(resp. inner) bounds for the capacity region of the original noisy network.
Based on the network equivalence framework, this paper presents scalable upper
and lower bounding models for wireless networks with potentially many nodes. A
channel decoupling method is proposed to decompose wireless networks into
decoupled multiple-access channels (MACs) and broadcast channels (BCs). The
upper bounding model, consisting of only point-to-point bit pipes, is
constructed by firstly extending the "one-shot" upper bounding models developed
by Calmon et al. and then integrating them with network equivalence tools. The
lower bounding model, consisting of both point-to-point and point-to-points bit
pipes, is constructed based on a two-step update of the lower bounding models
to incorporate the broadcast nature of wireless transmission. The main
advantages of the proposed methods are their simplicity and the fact that they
can be extended easily to large networks with a complexity that grows linearly
with the number of nodes. It is demonstrated that the resulting upper and lower
bounds can approach the capacity in some setups.
