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Future mobile broadband networks are characterized with high data rate and improved coverage, which will enable real-time video multicast and broadcast services. Scalable video coding (SVC), combined with adaptive modulation and coding schemes (MCS) and wireless multicast, provides an excellent solution for streaming video to heterogeneous wireless devices. By choosing different MCSs for different video layers, SVC can provide good video quality to users in good channel conditions while maintaining basic video quality for users in bad channel conditions. A key issue to apply SVC to wireless multicast streaming is to choose appropriate MCS for each video layer and to determine the optimal resource allocation among multiple video sessions. We formulate this problem as total utility maximization, subject to the constraint of available radio resources. We prove that the formulated problem is NP-hard and propose an optimal, two-step dynamic programming solution with pseudo-polynomial time complexity. Simulation results show that our algorithm offers significant improvement on the video quality over a naive algorithm and an adapted greedy algorithm, especially in the scenarios with multiple real video sequences and limited radio resources.