  Two outer bounds on the admissible source region for broadcast channels with
correlated sources are presented: the first one is strictly tighter than the
existing outer bound by Gohari and Anantharam while the second one provides a
complete characterization of the admissible source region in the case where the
two sources are conditionally independent given the common part. These outer
bounds are deduced from the general necessary conditions established for the
lossy source broadcast problem via suitable comparisons between the virtual
broadcast channel (induced by the source and the reconstructions) and the
physical broadcast channel.
