On the joint design of compressed sensing and network coding for wireless communications

Compressed sensing and network coding techniques have seen a widespread interest in many disciplines during the last decade. Recently, a novel idea emerged for the combination of these areas in wireless communications to leverage the benefits from network coding while taking advantage of the correlations in the (sensory) data. The potential gains, such as lower latency for large-scale sensing scenarios, reduced energy consumption, and a decrease in the amount of data during transmissions, are alluring to many use-cases. However, a common issue one faces when joining both techniques is encountered in the fact that network coding is designed to operate over finite fields, whereas compressed sensing is mainly concerned with real numbers. This paper studies the impact of compressed sensing on network coding to enable one step decoding for the reconstruction of compressed data. We emphasize and discuss the design of the sensing and coding matrices, as well as the algorithms that enable accurate reconstructions. We employ the KL1p compressed sensing library and the NS3 simulator to evaluate this joint design. Our simulations show that using normalized coefficient matrices drawn from Gaussian distributions has higher efficiency and scalability including, but not limited to, multi-hop networks, where the recoding feature of network coding can be exploited. Furthermore, the Subspace Pursuit algorithm outperforms the state-of-the-art reconstruction algorithms, with respect to the reconstruction signal-to-noise ratio, by more than two folds compared to the other benchmark algorithms in cluster-based Wireless Sensor Networks, where recoding using real network codes are involved.