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In this paper, we propose a utility-based resource allocation scheme for layer-encoded IPTV multicast streaming service over IEEE 802.16 WiMAX networks. Unlike existing utility-based schemes, this mechanism is designed for wireless networks which support adaptive modulation and coding. Each video stream (or program) is encoded into different layers. Then, our mechanism adjusts the number of each user's received layers dynamically according to its channel condition and the available network bandwidth, so as to maximize total utility. We prove that this problem is NP-hard, and show that our scheme is bounded in performance to the optimal solution and can run in polynomial time. The simulation results show that this scheme can allocate resource flexibly according to the utility function of each program, the popularity of each program (i.e., the number of users receiving each program), and the amount of total available resource in the network. The result also shows that the fairness of the system can be guaranteed.