We develop a mathematical framework for the extrinsic information transfer (EXIT) analysis to assess the convergence behavior of maximum a posteriori (MAP)-based joint iterative decoding of correlated sources, which are separately encoded and transmitted over noisy channels. Unlike the previous work, our approach focuses on the case side information about the correlation is not perfectly given at the joint decoder but is extracted from decoder output and updated in an iterative manner. The presented framework provides a convenient way to compare between schemes. We show that it allows us to easily and accurately predict joint decoding gain and turbo cliff position.