Distributed Estimation; Three Theorems

In distributed coding of two correlated discrete sources, the objective is to reconstruct the sources' symbols at a common decoder. In contrast, in distributed estimation the main goal of coding is to protect the relevant information about the source parameters of interest. Thus it is useful to determine the rates under which the distributed estimator can achieve the same accuracy as it can in local estimation. In this paper we show that for fixed parameters, the rates in the Slepian-Wolf region is not only sufficient but also necessary for efficient estimation. The simple proof based on the method of types and large deviation theory leads to derivation of a lower-bound on the region of rates for a large class of bivariate sources.