This paper considers a framework where data from correlated sources are
transmitted with help of network coding in ad-hoc network topologies. The
correlated data are encoded independently at sensors and network coding is
employed in the intermediate nodes in order to improve the data delivery
performance. In such settings, we focus on the problem of reconstructing the
sources at decoder when perfect decoding is not possible due to losses or
bandwidth bottlenecks. We first show that the source data similarity can be
used at decoder to permit decoding based on a novel and simple approximate
decoding scheme. We analyze the influence of the network coding parameters and
in particular the size of finite coding fields on the decoding performance. We
further determine the optimal field size that maximizes the expected decoding
performance as a trade-off between information loss incurred by limiting the
resolution of the source data and the error probability in the reconstructed
data. Moreover, we show that the performance of the approximate decoding
improves when the accuracy of the source model increases even with simple
approximate decoding techniques. We provide illustrative examples about the
possible of our algorithms that can be deployed in sensor networks and
distributed imaging applications. In both cases, the experimental results
confirm the validity of our analysis and demonstrate the benefits of our low
complexity solution for delivery of correlated data sources