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Scalable video coding (SVC) and Adaptive Modulation and Coding (AMC) are two key techniques for video multicast in broadband wireless networks. They can improve the system performance by enhancing the wireless resource allocation schemes and assigning appropriate modulation and coding schemes (MCS) to different layers of scalable video sequences. We formulate the problem as maximizing the total system utility subject to the total resource constraint, where the utility of each user is a generic non-negative, non-decreasing function of received rate. We then propose a fast intra-session MCS assignment algorithm based on dynamic programming. This algorithm can be integrated with an existing inter-session resource allocation algorithm and applied to multi-session scenarios. Simulation results show that our algorithm achieves significant improvement on the video quality over a naive algorithm and an adapted greedy algorithm, and greatly reduces the running time in both single-session and multi-session scenarios compared to a former optimal algorithm.