In this paper, we would like to investigate the optimal wireless streaming of a multi-quality tiled 360 virtual reality (VR) video from a server to multiple users. To this end, we propose to maximally exploit potential multicast opportunities by effectively utilizing characteristics of multi-quality tiled 360 VR videos and computation resources at the users' side. In particular, we consider two requirements for quality variation in one field-of-view (FoV), i.e., the absolute smoothness requirement and the relative smoothness requirement, and two video playback modes, i.e., the direct-playback mode (without user transcoding) and transcode-playback mode (with user transcoding). Besides natural multicast opportunities, we introduce two new types of multicast opportunities, namely, relative smoothness-enabled multicast opportunities, which allow a flexible tradeoff between viewing quality and communications resource consumption, and transcoding-enabled multicast opportunities, which allow a flexible tradeoff between computation and communications resource consumptions. Then, we establish a novel mathematical model that reflects the impacts of natural, relative smoothness-enabled, and transcoding-enabled multicast opportunities on the average transmission energy and transcoding energy. Based on this model, we optimize the transmission resource allocation, playback quality level selection, and transmission quality level selection to minimize the energy consumption in the four cases with different requirements for quality variation and video playback modes. By comparing the optimal values in the four cases, we prove that the energy consumption reduces when more multicast opportunities can be utilized. Finally, numerical results show substantial gains of the proposed solutions over existing schemes, and demonstrate the importance of exploiting of the three types of multicast opportunities.

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.

A 360 virtual reality (VR) video, recording a scene of interest in every direction, provides VR users with immersive viewing experience. However, transmission of a 360 VR video which is of a much larger size than a traditional video to mobile users brings a heavy burden to a wireless network. In this paper, we consider multi-quality multicast of a 360 VR video from a single server to multiple users using time division multiple access (TDMA). To improve transmission efficiency, tiling is adopted, and each tile is pre-encoded into multiple representations with different qualities. We optimize the quality level selection, transmission time allocation and transmission power allocation to maximize the total utility of all users under the transmission time and power allocation constraints as well as the quality smoothness constraints for mixed-quality tiles. The problem is a challenging mixed discrete-continuous optimization problem. We propose two low-complexity algorithms to obtain two suboptimal solutions, using continuous relaxation and DC programming, respectively. Finally, numerical results demonstrate the advantage of the proposed solutions.