  This paper considers the problem of reducing the broadcast decoding delay of
wireless networks using instantly decodable network coding (IDNC) based
device-to-device (D2D) communications. In a D2D configuration, devices in the
network can help hasten the recovery of the lost packets of other devices in
their transmission range by sending network coded packets. Unlike previous
works that assumed fully connected network, this paper proposes a partially
connected configuration in which the decision should be made not only on the
packet combinations but also on the set of transmitting devices. First, the
different events occurring at each device are identified so as to derive an
expression for the probability distribution of the decoding delay. The joint
optimization problem over the set of transmitting devices and the packet
combinations of each is, then, formulated. The optimal solution of the joint
optimization problem is derived using a graph theory approach by introducing
the cooperation graph and reformulating the problem as a maximum weight clique
problem in which the weight of each vertex is the contribution of the device
identified by the vertex. Through extensive simulations, the decoding delay
experienced by all devices in the Point to Multi-Point (PMP) configuration, the
fully connected D2D (FC-D2D) configuration and the more practical partially
connected D2D (PC-D2D) configuration are compared. Numerical results suggest
that the PC-D2D outperforms the FC-D2D and provides appreciable gain especially
for poorly connected networks.
