  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.
