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This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy. Also included are examples of computation and approximation of the divergence, and the demonstration of properties that are useful when one quantifies model uncertainty. 

Streaming of live 360-degree video allows users to follow a live event from any view point and has already been deployed on some commercial platforms. However, the current systems can only stream the video at relatively low-quality because the entire 360-degree video is delivered to the users under limited bandwidth. In this paper, we propose to use the idea of "flocking" to improve the performance of both prediction of field of view (FoV) and caching on the edge servers for live 360-degree video streaming. By assigning variable playback latencies to all the users in a streaming session, a "streaming flock" is formed and led by low latency users in the front of the flock. We propose a collaborative FoV prediction scheme where the actual FoV information of users in the front of the flock are utilized to predict of users behind them. We further propose a network condition aware flocking strategy to reduce the video freeze and increase the chance for collaborative FoV prediction on all users. Flocking also facilitates caching as video tiles downloaded by the front users can be cached by an edge server to serve the users at the back of the flock, thereby reducing the traffic in the core network. We propose a latency-FoV based caching strategy and investigate the potential gain of applying transcoding on the edge server. We conduct experiments using real-world user FoV traces and WiGig network bandwidth traces to evaluate the gains of the proposed strategies over benchmarks. Our experimental results demonstrate that the proposed streaming system can roughly double the effective video rate, which is the video rate inside a user's actual FoV, compared to the prediction only based on the user's own past FoV trajectory, while reducing video freeze. Furthermore, edge caching can reduce the traffic in the core network by about 80%, which can be increased to 90% with transcoding on edge server.