Some comments on the generalized Shannon lower bound for stationary finite-alphabet sources with memory (Corresp.)

We consider a class of strictly stationary binary sources
\{u_n, n \geq 1\}
, characterized by joint conditional probability mass functions \begin{equation} Q_n(U_n = k_n \mid \theta) = \prod_{i=1}^n \theta^{1-k_i} (1 - \theta)^{k_i} \end{equation} for all
n \geq 1
, where
\theta
is an r.v. on