Algorithm 1 Extended AB algorithm for the optimization problem (2)

Input:  $p\left(y\right|x,s)$, $p\left(z\right|x,s)$, $p\left(s\right)$.   1:Compute $D_{min}$ and $D_{max}$ and select $D\in [D_{min},D_{max}]$.   2:Initialize $p(u,x),c(u,z)$.   3:while not converge do   4:   Update $q\left(x\right|u,y,s)$ and $q\left(u\right|z)$ based on (9).   5:   Solve $\lambda$ based on the equation (13).   6:   Update $p(u,x)$ based on (12).   7:   Update $c(u,z)$ based on (10).   8:end while Output:  $p(u,x)$.