On the benefits of network coding to compressive data gathering in wireless sensor networks

We investigate the joint application of compressive sensing and network coding to the problem of energy efficient data gathering in wireless sensor networks. We consider the problem of optimally constructing forwarding trees to carry compressed data to projection nodes; each compressed data refers to a weighted aggregation of measurements from sensors collected at one projection node. Projection nodes then forward their received compressed data to the sink, which subsequently recovers the original measurements. This aggregation technique based on compressive sensing is shown to reduce significantly the number of transmissions. We observe that the presence of multiple forwarding trees gives rise to many-to-many communication patterns which in turn can be exploited to perform network coding on the compressed data being forwarded on these trees. Such technique will further reduce the number of transmissions required to gather the measurements, and consequently result in a better network-wide energy efficiency. This paper addresses the problem of network coding aware construction of forwarding/aggregation trees and we present a mathematical model to optimally construct such trees. We also develop a decentralized method for solving the problem and we show that our method is both very scalable and accurate. We also show that when both network coding and compressive data gathering are considered jointly, modest gains may be attained.