Traditionally, communication networks are composed of
routing nodes, which relay and duplicate data. Work in
recent years has shown that for the case of multicast, an
improvement in both rate and code-construction complexity can be
gained by replacing these routing nodes by linear coding
nodes. These nodes transmit linear combinations of the inputs
transmitted to them.
In this work, we deal with bounds on the alphabet size of
linear codes for multicast. We show both lower and upper bounds as
a function of sink-set size and graph topology. We show that these
bounds apply, as well, to a special case of multicast,
static broadcast. We also show how node-memory addition
can increase the effective alphabet-size available for coding.
We have included a section on the number of nodes in which coding
is required, as a function of the number of terminals and their rates.
