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This paper considers the problem of reducing the broadcast decoding delay of wireless networks using instantly decodable network coding- based device-to-device communications. In contrast with the previous works that assume a fully connected network, this paper investigates a partially connected configuration in which multiple devices are allowed to transmit simultaneously. To that end, different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. Afterward, the joint optimization problem over the set of transmitting devices and packet combination of each is formulated. The optimal solution of the joint optimization problem is derived using a graph-theoretic approach by introducing the cooperation graph in which each vertex represents a transmitting device with a weight translating its contribution to the network. This paper solves the …