In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the upper bound on the probability of decoding error as a function of the system parameters. We also establish the sufficient conditions on the number of network coded symbols required to achieve decoding error probability below a certain level. We then propose a low complexity iterative decoding algorithm based on message passing for decoding the network coded data of a particular class of statistically dependent sources that present pairwise linear correlation. The algorithm operates on a graph that captures the network coding constraints, while the knowledge about the source correlation is directly incorporated in the messages exchanged over the graph. We test the proposed method on both synthetic data and correlated image sequences and demonstrate that the prior knowledge about the source correlation can be effectively exploited at the decoder in order to provide a good reconstruction of the transmitted data in cases where the network coded data available at the decoder is not sufficient for exact decoding.