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Emerging wireless multicast applications simultaneously impose two requirements to the underlying communication networks: to provide sufficient bandwidth and to support a variety of quality-of-service (QoS) sensitivities. For the first requirement, network coding has been proposed recently as an effective way of improving bandwidth utilization. However, almost all previous works about network coding focus on the throughput gain without considering the QoS requirements. Optimal network code construction in wireless multicast under different QoS constraints remains as a significant challenge. In this research, we study the QoS-driven network coding problem. We use large deviation principle to establish the relationship among source rate, link condition, QoS requirement, and network code. Using this relationship, under given QoS requirements, we solve the optimal network code construction problem. The proposed network code supports maximal source rate without violating the QoS requirements. These results constitute the foundations for future designing and implementing network coding based wireless multicast protocols.