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.

Abstract-Accurate and efficient measurement of networkinternal characteristics is critical for the management and maintenance of large-scale networks. In this paper, we propose a linear algebraic network tomography (LANT) framework for the active inference of link loss rates on mesh topologies through network coding. Probe packets are transmitted from the sources to the destinations along a set of paths. Intermediate nodes linearly combine the received probes and transmit the coded probes using predetermined coding coefficients. Although a smaller probe size can reduce the bandwidth usage of the network, the inference framework is not valid if the probe size falls below a certain threshold. To this end, we determine the minimum probe packet size, which is necessary and sufficient to establish the mapping between the contents of the received probes and the losses on the different sets of paths. Then, we develop algorithms to find the coding coefficients such that the minimum probe size is achieved. We propose a linear algebraic approach to develop consistent estimators of link loss rates, which converge to the actual loss rates as the number of probes increases. Simulation results show that the LANT framework achieves better estimation accuracy than the belief propagation algorithm for a large number of probe packets.

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