  This paper studies the application of compute-and-forward to multiple access
relay channels (MARC). Despite its promising advantage of improving network
throughput, it is not straightforward to apply compute-and-forward to the MARC.
This paper proposes two efficient cooperation strategies for the MARC with
compute-and-forward. Both proposed strategies are opportunistic in the sense
that the cooperation between the relay and the destination are performed only
when it is needed for the sake of high transmission efficiency. In the first
strategy, the relay helps the destination by sending its local optimal integer
coefficient vector without taking into account that the resulting integer
coefficient matrix at the destination is full rank. In contrast, in the second
strategy, the relay forwards its ``best'' coefficient vector that always
ensures a full rank coefficient matrix at the destination. Both of the proposed
strategies achieve twice the network throughput of the existing strategies at
high signal-to-noise power ratio (SNR). They also have lower outage
probability, independent of relay placement. Furthermore, the first strategy
nearly achieves diversity gain of order two, and the second one achieves
exactly the diversity gain of order two, which cannot be achieved by the
existing strategies.
