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Scalable video coding (SVC), together with adaptive modulation and coding (AMC), can improve wireless multicast streaming video by jointly performing radio resource allocation and modulation and coding scheme (MCS) selection. However, the existing schemes in the literature allocate radio resources for different video layers separately, which leads to a waste of radio resources. In this work, we introduce the notion of joint layer resource allocation which allows to jointly allocate resources to multiple video layers that are assigned the same MCS. We formulate this problem and prove it to be NP-hard. Then we develop a pseudo-polynomial algorithm that finds the optimal total system utility. Our algorithm assumes a very generic utility function and flexible video layer rates. To reduce the complexity of the algorithm, we also propose Fully Polynomial Time Approximation Schemes (FPTAS) for the same problem. Simulation results show that our optimal algorithm offers significant improvement on system utility over a previous optimal algorithm and a greedy algorithm both of which do not support joint layer resource allocation. The proposed approximation algorithm provides controllable tradeoff between performance and computational complexity and, with appropriately chosen parameters, it outperforms the greedy algorithm with 40% less running time.