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In this paper, we study the resource allocation problem in a K-user wireless broadcast system with N-layer superposition coding (SPC). The problem is formulated as a sumutility maximization problem based on the average throughput. Using stochastic approximation, iteratively solving an approximated problem yields the optimality. The approximated problem can be solved by selecting the user group with the maximal weighted-sum-rate, which has a high computational complexity. Two low-complexity suboptimal algorithms are proposed. The simulation results show that the SPC gain highly depends on the variability of the channel and the SNR range of users. SPC is more favourable in the scenario with small-variation fast-fading channel and a large SNR range of users. The performance of the proposed low-complexity algorithms are close to the optimal solution, and the SPC gain achieved is substantial.