In many practical distributed source coding (DSC) applications, correlation information has to be estimated at the encoder in order to determine the encoding rate. Coding efficiency depends strongly on the accuracy of this correlation estimation. While error in estimation is inevitable, the impact of estimation error on compression efficiency has not been sufficiently studied for the DSC problem. In this paper, we study correlation estimation subject to rate and complexity constraints, and its impact on coding efficiency in a DSC framework for practical distributed image and video applications. We focus on, in particular, applications where binary correlation models are exploited for Slepian-Wolf coding and sampling techniques are used to estimate the correlation, while extensions to other correlation models would also be briefly discussed. In the first part of this paper we investigate the compression of binary data. We first propose a model to characterize the relationship between t...