}$ into an action sequence $A^{n};$ two decoders, namely $$\mathrm{h}_{0}\text{: }[0,0^{nR_{0}}]\times\mathcal{Y}^{n}\rightarrow\mathcal{\hat{X}}_{0}^{n},\label{decoder0}$$ which maps the message $M_{0}$ and the measured sequence $Y^{n}$ into the estimated sequence $\hat{X}_{0}^{n};$ $$\mathrm{h}_{0}\text{: }[0,0^{nR_{0}}]\times\mathcal{Z}^{n}\rightarrow\mathcal{\hat{X}}_{0}^{n},\label{decoder0}$$ which maps the message $M_{0}$ and the measured sequence $