  We study the problem of simulating a two-user multiple access channel over a
multiple access network of noiseless links. Two encoders observe independent
and identically distributed (i.i.d.) copies of a source random variable each,
while a decoder observes i.i.d. copies of a side-information random variable.
There are rate-limited noiseless communication links and independent pairwise
shared randomness resources between each encoder and the decoder. The decoder
has to output approximately i.i.d. copies of another random variable jointly
distributed with the two sources and the side information. We are interested in
the rate tuples which permit this simulation. This setting can be thought of as
a multi-terminal generalization of the point-to-point channel simulation
problem studied by Bennett et al. (2002) and Cuff (2013). General inner and
outer bounds on the rate region are derived. For the specific case where the
sources at the encoders are conditionally independent given the
side-information at the decoder, we completely characterize the rate region.
Our bounds recover the existing results on function computation over such
multi-terminal networks. We then show through an example that an additional
independent source of shared randomness between the encoders strictly improves
the communication rate requirements, even if the additional randomness is not
available to the decoder. Furthermore, we provide inner and outer bounds for
this more general setting with independent pairwise shared randomness resources
between all the three possible node pairs.
