Node 2 and Node 3 so as to take concerted actions in order to affect the side information sequences. We assume the action sequence taken by Node 2 and Node 3 to be a function of only the broadcast message $M_{b}$ sent over the broadcast link of rate $R_{b}$.

The problem is defined by the pmfs $p_{X}(x)$, $p_{YZ|AX}(y,z|a,x)$ and discrete alphabets $\mathcal{X},\mathcal{Y},{\cal Z},\mathcal{A},$ $\mathcal{\hat{X}}_{1},\mathcal{\hat{X}}_{2},$ as follows. The source sequence $X^{n}$ with $X^{n}\in\mathcal{X}^{n}$ is i.i.d. with pmf $p_{X}(x)$. Node 1 measures sequence $X^{n}$ and encodes it into messages $M_{1}$ and $M_{b}$ of $nR_{1}$ and $nR_{b}$ bits, respectively, which are delivered to Node 2. Moreover, message $M_{b}$ is broadcast also to Node 3. Node 2 estimates a sequence $\hat{X}_{1}^{n}\in\mathcal{\hat{X}}_{1}^{n}$ and Node 3 estimates a sequence $\hat{X}_{2}^{n}\in\mathcal{\hat{X}}_{2}^{n}$. To this end, Node 2 receives messages $M_{1}$ and $M_{b}$ and, based only on the latter message, it selects an action sequence $A^{n},$ where $A^{n}\in\mathcal{A}^{n}.$ Node 2 maps messages $M_{1}$ and $M_{b}$, received from Node 1, and the locally available sequence $Y^{n}$ in a message $M_{2}$ of $nR_{2}$ bits, which is delivered to Node 3. Node 3 receives messages $M_{2}$ and $M_{b}$ and based only on the latter message, it selects an action sequence $A^{n},$ where 