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Optimal Network Coding Policy for Joint Cellular and Intermittently Connected D2D Networking

In this paper, we study the problem of transmittinga common content to a number of cellular users with the help of device-to-device (D2D) links via instantly decodable network coding (IDNC). In particular, a common content that is broadcast by a base station may be partially received by cellular users due to packet erasures over cellular links. D2D links among cellular users, which may be intermittently available due to mobility and link imperfections, are used to recover the missing content. In this setup, we design an IDNC mechanism to minimize packet completion time, defined as the amount of time it takes for the common content to be received by all cellular users. We develop an optimal packet completion time strategy by constructing a two-layer IDNC conflict graph where the higher layer represents all feasible network coded packets that can be transmitted over cellular links, while the lower layer consists of network coded packets (as well as corresponding cellular users that can generate and transmit these packets) that can be transmitted via D2D links. We show that finding the optimal IDNC packets to minimize the packet completion time problem is equivalent to finding the maximum independent set of the two-layer IDNC conflict graph. We also design a sub-optimal IDNC mechanism, aIDNC, that efficiently finds IDNC packets to be transmitted over cellular and D2D links. Finally, the efficiency of our proposed approach is verified through numerical experiments.