  This paper considers the multiple-access relay channel in a setting where two
source nodes transmit packets to a destination node, both directly and via a
relay node, over packet erasure channels. Intra-session network coding is used
at the source nodes and inter-session network coding is employed at the relay
node to combine the recovered source packets of both source nodes. In this
work, we investigate the performance of the network-coded system in terms of
the probability that the destination node will successfully recover the source
packets of the two source nodes. We build our analysis on fundamental
probability expressions for random matrices over finite fields and we derive
upper bounds on the system performance for the case of systematic and
non-systematic network coding. Simulation results show that the upper bounds
are very tight and accurately predict the decoding probability at the
destination node. Our analysis also exposes the clear benefits of systematic
network coding at the source nodes compared to non-systematic transmission.
