  This paper considers a multi-source multi-relay network, in which relay nodes
employ a coding scheme based on random linear network coding on source packets
and generate coded packets. If a destination node collects enough coded
packets, it can recover the packets of all source nodes. The links between
source-to-relay nodes and relay-to-destination nodes are modeled as packet
erasure channels. Improved bounds on the probability of decoding failure are
presented, which are markedly close to simulation results and notably better
than previous bounds. Examples demonstrate the tightness and usefulness of the
new bounds over the old bounds.
