Accurate and efficient measurement of network-internal 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.
['Jiaqi Gui', 'Vahid Shah-Mansouri', 'Vincent W. S. Wong']
Accurate and Efficient Network Tomography Through Network Coding