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We propose a cross-layer design framework for efficient broadcasting scalable H.264 videos over the downlink multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing systems. The objective is to maximize the average peak signal-to-noise ratio of the received video streams by jointly optimizing video layer extraction, subcarrier allocation, modulation and coding, and transmit precoding, considering the heterogeneity of video sources and channel conditions. Specifically, to exploit the MIMO channel, we employ a codebook-based linear transmit precoding strategy with limited feedback. Given the fact that different quality layers of the video have different importance, we propose an adaptive modulation and coding scheme, where a fixed coding rate is used for each quality layer and unequal error protection is implemented for different layers. We further propose a subcarrier allocation strategy to assign transmission channels for different layers of different users' videos, to satisfy the decoding dependence constraints among the video layers and to maximize the reconstructed video quality. The proposed scalable video broadcast solution has a low complexity and low signaling overhead, which makes it suitable for practical implementations. We provide experimental results to demonstrate the effectiveness of the proposed solution, using both model-based simulations and an end-to-end software simulation testbed.