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A Superposition Coding (SC) scheme using discrete Adaptive Modulation (AM) for a three-node wireless relay system is proposed. In the proposed method, 2/4-QAM and 4/16-QAM hierarchical modulations are used to generate the SC message composed of a basic and superposed messages. We derive the analytical throughput expression of the system and determine the necessary conditions for guaranteeing optimal power allocation. The simulation results show that the proposed power allocation achieves a throughput close to the one obtained by exhaustive search. Moreover, over a large range of SNRs, the proposed method largely outperforms the conventional relaying methods such as multi-hop and cooperative diversity, proving the substantial benefits of SC even under practical discrete AM and decoding errors during SIC.