Delay Reduction in Multi-Hop Device-to-Device Communication using   Network Coding
  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. 
Ahmed Douik, Sameh Sorour, Tareq Y. Al-Naffouri, Hong-Chuan Yang,   Mohamed-Slim Alouini
cs.IT math.IT