  In this paper, we study the contribution of network coding (NC) in improving
the multicast capacity of random wireless ad hoc networks when nodes are
endowed with multi-packet transmission (MPT) and multi-packet reception (MPR)
capabilities. We show that a per session throughput capacity of
$\Theta(nT^{3}(n))$, where $n$ is the total number of nodes and T(n) is the
communication range, can be achieved as a tight bound when each session
contains a constant number of sinks. Surprisingly, an identical order capacity
can be achieved when nodes have only MPR and MPT capabilities. This result
proves that NC does not contribute to the order capacity of multicast traffic
in wireless ad hoc networks when MPR and MPT are used in the network. The
result is in sharp contrast to the general belief (conjecture) that NC improves
the order capacity of multicast. Furthermore, if the communication range is
selected to guarantee the connectivity in the network, i.e., $T(n)\ge
\Theta(\sqrt{\log n/n})$, then the combination of MPR and MPT achieves a
throughput capacity of $\Theta(\frac{\log^{{3/2}} n}{\sqrt{n}})$ which provides
an order capacity gain of $\Theta(\log^2 n)$ compared to the point-to-point
multicast capacity with the same number of destinations.
