  We consider a wireless distributed computing system, in which multiple mobile
users, connected wirelessly through an access point, collaborate to perform a
computation task. In particular, users communicate with each other via the
access point to exchange their locally computed intermediate computation
results, which is known as data shuffling. We propose a scalable framework for
this system, in which the required communication bandwidth for data shuffling
does not increase with the number of users in the network. The key idea is to
utilize a particular repetitive pattern of placing the dataset (thus a
particular repetitive pattern of intermediate computations), in order to
provide coding opportunities at both the users and the access point, which
reduce the required uplink communication bandwidth from users to access point
and the downlink communication bandwidth from access point to users by factors
that grow linearly with the number of users. We also demonstrate that the
proposed dataset placement and coded shuffling schemes are optimal (i.e.,
achieve the minimum required shuffling load) for both a centralized setting and
a decentralized setting, by developing tight information-theoretic lower
bounds.
