Analog network coding

Abstract – Network coding has been shown to improve throughput and reliability in a variety of theoretical and prac-tical settings. But it has had limited success in areas like sen-sor networks due to it’s two limitations. First, network codes are ”all-or-nothing ” codes; the sink cannot decode any in-formation unless it receives as many coded packets as the original number of packets. Second, sensor networks often measure physical signals which show a high degree of spa-tial correlation; present network coding techniques cannot perform in-network lossy compression to take advantage of the spatial correlation. This paper presents ”Real ” Network Codes that are linear over real fields. We build on recent results from Compressed Sensing to develop new codes which can be decoded to get progressively more accurate approximations as more coded packets are received at the sink. Further, they can compress distributed correlated data inside the network without requir-ing that the nodes know how the data is correlated. Thus, Real Network Codes combine two exciting but hitherto sep-arate areas, Network Coding and Compressed Sensing, al-lowing them to keep the advantages of network coding, but also make them capable of finding low distortion approxima-tions with partial information and perform distributed com-pression of correlated data.