  Consider a device-to-device (D2D) fog-radio access network wherein a set of
devices are required to store a set of files. Each device is connected to a
subset of the cloud data centers and thus possesses a subset of the data. This
paper investigates the problem of disseminating all files among the devices
while reducing the total time of communication, i.e., the completion time,
using instantly decodable network coding (IDNC). While previous studies on the
use of IDNC in D2D systems assume a fully connected communication network, this
paper tackles the more realistic scenario of a partially connected network in
which devices can only target devices in their transmission range. The paper
first formulates the optimal joint optimization of selecting the transmitting
device(s) and the file combination(s) and exhibits its intractability. The
completion time is approximated using the celebrated decoding delay approach by
deriving the relationship between the quantities in a partially connected
network. The paper introduces the cooperation graph and demonstrates that the
relaxed problem is equivalent to a maximum weight clique problem over the newly
designed graph wherein the weights are obtained by solving a similar problem on
the local IDNC graphs. Extensive simulations reveal that the proposed solution
provides noticeable performance enhancement and outperforms previously proposed
IDNC-based schemes.
