such that the pairs $(X_{i},Y_{i})$ for $i\in[1,n]$ are independent and identically distributed (i.i.d.) with joint pmf $p_{XY}(x,y)$. Node 1 measures sequences $X^{n}$ and $Y^{n}$ and encodes them in a message $M_{1}$ of $nR_{1}$ bits, which is delivered to Node 2. Node 2 estimates a sequence $\hat{X}_{1}^{n}\in\mathcal{\hat{X}}_{1}^{n}$ within given distortion requirements to be discussed below. Moreover, Node 2 maps the message $M_{1}$ 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 wishes to estimate a sequence $\hat{X}_{2}^{n}\in\mathcal{\hat{X}}_{2}^{n}$ within given distortion requirements. To this end, Node 3 receives message $M_{2}$ and based on this, it selects an action sequence $A^{n},$ where $A^{n}\in\mathcal{A}^{n}.$ The action sequence affects the quality of the measurement $Z^{n}$ of sequence $Y^{n}$ obtained at the Node 3. Specifically, given $A^{n}$ and $Y^{n}$, the sequence $Z^{n}$ is distributed as $p(z^{n}|a^{n},y^{n})=\prod_{i=1}^{n}p_{Z|A,Y}(z_{i}|y_{i},a_{i})$. The cost of the action sequence is defined by a cost function $\Lambda$: $\mathcal{A\rightarrow}[0,\Lambda_{\max}]$ with $0\leq\Lambda_{\max}<\infty,$ as $\Lambda(a^{n})=\sum_{i=1}^{n}\Lambda(a_{i})$. The estimated sequence $\hat{X}_{2}^{n}$ with $\hat{X}_{2}^{n}\in\mathcal{\hat{X}}_{2}^{n}$ is then obtained as a function of $M_{2}$ and $Z^{n}$. The estimated sequences $\hat{X}_{j}^{n}$ for $j=1,2$ must satisfy distortion constraints defined by functions $d_{j}(x,\hat{x}_{j})$: $\mathcal{X}\times\mathcal{\hat{X}}_{j}\rightarrow[0,D_{\max}]$ with $0\leq D_{\max}<\infty$ for $j=1,2,$ 