The multiple-access relay channel (MARC) based on network coding has been proposed in recent papers as a means to achieve diversity gain in wireless networks, at the same time reducing the number of transmissions by a relay node. In MARC, multiple sources transmit to a common destination with the assistance of a single relay. In a network-coding-based realization of MARC, the relay merges the messages received from the two sources and forwards them to the destination; at the destination, the sources' messages can be recovered from either their direct transmissions or by performing additional network coding. In this work, performance analysis in the form of outage probability and coverage area, when non-ideal source-relay links exist, is performed. The relay is assumed to operate either in static or adaptive mode, and comparisons with the conventional MARC and point-to-point transmission are made. The outage results show that the conventional MARC system perform better when the source-relay links are high quality. Network-coding- based MARC operated in adaptive mode has better performance when the quality of the source-relay links are poor, and this system has better coverage area.