A Coding Theorem for Multiterminal Estimation

In this paper a coding theorem for multiterminal estimation is presented. The theorem is a generalization of the distributed coding theorem first proved by Slepian and Wolf (1973), where the goal is to estimate the joint probability distribution of correlated sources, rather than to reconstruct them at the receiver. For this, it is shown first that the joint-type of the received sequences is a sufficient statistic for estimation. Then, it is proved that for sufficiently large sequences, only a sum-rate lower bounded by the mutual information of the correlated sources is "sufficient" to perfectly reconstruct the sufficient statistic at the receiver. Simulation results for the special case of estimation with side information at the receiver is provided