This paper considers the problem of reducing the broadcast decoding delay ofwireless networks using instantly decodable network coding (IDNC) baseddevice-to-device (D2D) communications. In a D2D configuration, devices in thenetwork can help hasten the recovery of the lost packets of other devices intheir transmission range by sending network coded packets. Unlike previousworks that assumed fully connected network, this paper proposes a partiallyconnected configuration in which the decision should be made not only on thepacket combinations but also on the set of transmitting devices. First, thedifferent events occurring at each device are identified so as to derive anexpression for the probability distribution of the decoding delay. The jointoptimization problem over the set of transmitting devices and the packetcombinations of each is, then, formulated. The optimal solution of the jointoptimization problem is derived using a graph theory approach by introducingthe cooperation graph and reformulating the problem as a maximum weight cliqueproblem in which the weight of each vertex is the contribution of the deviceidentified by the vertex. Through extensive simulations, the decoding delayexperienced by all devices in the Point to Multi-Point (PMP) configuration, thefully connected D2D (FC-D2D) configuration and the more practical partiallyconnected D2D (PC-D2D) configuration are compared. Numerical results suggestthat the PC-D2D outperforms the FC-D2D and provides appreciable gain especiallyfor poorly connected networks.
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