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This research addresses the problem of robust linear video transmission over the Rayleigh fading channel, where only statistical channel state information (CSI) is available to the sender. We observe that discarding low-priority (LP) data and saving the channel uses for high-priority (HP) data can significantly improve the quality of the received video. We formulate an optimization problem that aims to minimize the total squared error of a multi-variant Gaussian random vector under the given bandwidth and power resources. To tame the complexity of this NP-hard problem, we analyze two sub-problems, namely power allocation and bandwidth allocation, and propose an iterative algorithm to approximate the solution. Subsequently, we propose a one-pass two-step fast algorithm that further reduces both algorithmic and computational complexity. A linear video transmission system is implemented based on the proposed algorithm. Simulations show that our system significantly outperforms Soft-Cast, and the PSNR gain at 5th percentile of 1000 test runs is between 4.0 dB and 7.5 dB under varying noise levels.