Approximate Decoding Approaches for Network Coded Correlated Data

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.