  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.
