In this paper, we study the server-side rate adaptation problem for streaming tile-based adaptive 360-degree videos to multiple users who are competing for transmission resources at the network bottleneck. Specifically, we develop a convolutional neural network (CNN)-based viewpoint prediction model to capture the nonlinear relationship between the future and historical viewpoints. A Laplace distribution model is utilized to characterize the probability distribution of the prediction error. Given the predicted viewpoint, we then map the viewport in the spherical space into its corresponding planar projection in the 2-D plane, and further derive the visibility probability of each tile based on the planar projection and the prediction error probability. According to the visibility probability, tiles are classified as viewport, marginal and invisible tiles. The server-side tile rate allocation problem for multiple users is then formulated as a non-linear discrete optimization problem to minimize the overall received video distortion of all users and the quality difference between the viewport and marginal tiles of each user, subject to the transmission capacity constraints and users specific viewport requirements. We develop a steepest descent algorithm to solve this non-linear discrete optimization problem, by initializing the feasible starting point in accordance with the optimal solution of its continuous relaxation. Extensive experimental results show that the proposed algorithm can achieve a near-optimal solution, and outperforms the existing rate adaptation schemes for tile-based adaptive 360-video streaming.
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