  In this paper, we propose two novel schemes to solve the problem of finding a
quasi-optimal number of coded packets to multicast to a set of independent
wireless receivers suffering different channel conditions. In particular, we
propose two network channel virtualization schemes that allow for representing
the set of intended receivers in a multicast group to be virtualized as one
receiver. Such approach allows for a transmission scheme not only adapted to
per-receiver channel variation over time, but to the network-virtualized
channel representing all receivers in the multicast group. The first scheme
capitalizes on a maximum erasure criterion introduced via the creation of a
virtual worst per receiver per slot reference channel of the network. The
second scheme capitalizes on a maximum completion time criterion by the use of
the worst performing receiver channel as a virtual reference to the network. We
apply such schemes to a GEO satellite scenario. We demonstrate the benefits of
the proposed schemes comparing them to a per-receiver point-to-point adaptive
strategy.
