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The multiple access relay channel (MARC) where multiple users send independent information to a single destination aided by a single relay under large-scale path loss and slow fading is investigated. At the beginning, the users take turns to transmit their packets. The relay is not aware of the erasure status of each packet at the destination but has the knowledge of the average signal-to-noise-ratio (SNR) of every communication link. With this knowledge, the relay applies network coded retransmission on the overheard packets so as to maximize the expected total number of recovered packets or minimize the average packet loss rate at the destination. Several network coding (NC) strategies at the relay are designed. In particular, for the case where the relay is given only one time slot for retransmission, an optimal NC construction is derived. For the multiple-slot case, three sub-optimal schemes are investigated, namely network coding with maximum distance separable (MDS) code (NC-MDS), the worst-user-first (WUF) scheme and a hybrid of NC-MDS and WUF. We prove that NC-MDS and WUF are asymptotically optimal in the high and low SNR regimes, respectively. A lower bound on the average packet loss rate has been derived. Numerical studies show that, in a cellular system, the hybrid scheme offers significant performance gain over a number of existing schemes in a wide range of SNR. We also observe that performance curves of both WUF and the hybrid scheme touch the derived lower bound in the low SNR regime.