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In multihop wireless networks, many applications require end-to-end reliable multicast communication with 100% packet delivery ratio. Recently, network coding has been applied to the reliable link-level multicast in wireless networks, where multiple lost packets with distinct intended receivers are XOR-ed together as one packet and forwarded via single retransmission, resulting in a significant reduction of bandwidth consumption in the scenarios of many receivers. However, the simple XOR operation cannot fully exploit the potential coding opportunities. Moreover, for the reliable multicast in multihop wireless networks, the number of receivers of link-level multicast is usually not large and thus this coding-based link-level multicast cannot provide a promising gain. In this work, we propose a new network coding-based reliable multicast scheme which exploits both network coding and the physical-layer broadcast nature. Specifically, first, at each link-level multicast the source node performs the more general coding operations instead of XOR and conducts the random linear packet coding such that more coding gain can be achieved. Second, each node snoops on all communications over the wireless medium and stores the overheard packets for packet decoding, such that an additional coding gain can be obtained. Extensive simulations demonstrate that the proposed scheme can greatly improve the transmission efficiency, especially in the case of large-group multicast.