Network Coding of Correlated Data with Approximate Decoding

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 network nodes for improved 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 capacity limits. We first show that the correlation between the data sources can be exploited at decoder by the design of a novel 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 approximate decoding performance improves when the accuracy of the correlation estimation increases even with simple approximate decoding techniques. We illustrate our algorithms in sensor networks and distributed video transmitting applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our solution for delivery of correlated data. Index Terms Network coding, approximate decoding, correlated data, distributed transmission, ad hoc networks.