  In this paper, the posterior matching scheme proposed by Shayevits and Feder
is extended to the Gaussian broadcast channel with feedback, and the error
probabilities and achievable rate region are derived for this coding strategy
by using the iterated random function theory. A variant of the Ozarow-Leung
code for the general two-user broadcast channel with feedback can be realized
as a special case of our coding scheme. Furthermore, for the symmetric Gaussian
broadcast channel with feedback, our coding scheme achieves the linear-feedback
sum-capacity like the LQG code and outperforms the Kramer code.
