  We consider the problem of broadcast with common messages, and focus on the
case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the
message intended for all the receivers in the set $\mathcal{A}$, is the same
for all the set $\mathcal{A}$ of the same cardinality. Instead of attempting to
characterize the capacity region of general broadcast channels, we only
consider the structure of the capacity region that any broadcast channel should
bear. The concept of latent capacity region is useful in capturing these
underlying constraints, and we provide a complete characterization of the
latent capacity region for the symmetric broadcast problem. The converse proof
of this tight characterization relies on a deterministic broadcast channel
model. The achievability proof generalizes the familiar rate transfer argument
to include more involved erasure correction coding among messages, thus
revealing an inherent connection between broadcast with common message and
erasure correction codes.
