A Linear Algebraic Approach for Loss Tomography in Mesh Topologies Using Network Coding

Abstract

Loss tomography aims to infer link loss rates using end-to-end measurements. We investigate active loss tomography on mesh topologies. When network coding is applied, based on the content of the received probe packet, a receiver should distinguish which paths have successfully transmitted a probe and which paths have not. We establish a lower bound on probe size which is necessary for obtaining such end-to-end observations. Furthermore, we propose a linear algebraic (LA) approach to developing consistent estimators of link loss rates. Our approach exploits the inherent correlation between the losses on links and the losses on different sets of paths, so that the estimators converge to the actual loss rates as the number of probes increases. We also prove that the identifiability of a link is a necessary and sufficient condition for the consistent estimation of its loss rate. Simulation results show that the LA approach achieves better estimation accuracy than the belief propagation (BP) algorithm, after sending reasonably sufficient probes.