In this paper, we would like to investigate fundamental impacts of multicast opportunities on efficient transmission of a 360 VR video to multiple users in the cases with and without transcoding at each user. We establish a novel mathematical model that reflects the impacts of multicast opportunities on the average transmission energy in both cases and the transcoding energy in the case with user transcoding, and facilitates the optimal exploitation of transcoding-enabled multicast opportunities. In the case without user transcoding, we optimize the transmission resource allocation to minimize the average transmission energy by exploiting natural multicast opportunities. The problem is nonconvex. We transform it to an equivalent convex problem and obtain an optimal solution using standard convex optimization techniques. In the case with user transcoding, we optimize the transmission resource allocation and the transmission quality level selection to minimize the weighted sum of the average transmission energy and the transcoding energy by exploiting both natural and transcoding- enabled multicast opportunities. The problem is a challenging mixed discrete-continuous optimization problem. We transform it to a Difference of Convex (DC) programming problem and obtain a suboptimal solution using a DC algorithm. Finally, numerical results demonstrate the importance of effective exploitation of transcoding-enabled multicast opportunities in the case with user transcoding.
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