We introduce a novel correlation model, called predictive Binary Symmetric Channel (BSC), for Distributed Source Coding (DSC). We then consider non-uniform binary sources and show that, for the predictive BSC model, the non-uniformity does not reduce the compression rate in asymmetric DSC. We assess the minimum achievable rate loss induced by a mismatch between the assumed and the true correlation models. We also propose an LDPC-based decoder adapted to both the classical (additive) BSC and the new (predictive) BSC correlation models. Finally, for Distributed Video Coding (DVC) application, we propose a criterion that allows us to switch between the two correlation models.