Passive network tomography uses end-to-end observations of network
communication to characterize the network, for instance to estimate the network
topology and to localize random or adversarial glitches. Under the setting of
linear network coding this work provides a comprehensive study of passive
network tomography in the presence of network (random or adversarial) glitches.
To be concrete, this work is developed along two directions: 1. Tomographic
upper and lower bounds (i.e., the most adverse conditions in each problem
setting under which network tomography is possible, and corresponding schemes
(computationally efficient, if possible) that achieve this performance) are
presented for random linear network coding (RLNC). We consider RLNC designed
with common randomness, i.e., the receiver knows the random code-books all
nodes. (To justify this, we show an upper bound for the problem of topology
estimation in networks using RLNC without common randomness.) In this setting
we present the first set of algorithms that characterize the network topology
exactly. Our algorithm for topology estimation with random network errors has
time complexity that is polynomial in network parameters. For the problem of
network error localization given the topology information, we present the first
computationally tractable algorithm to localize random errors, and prove it is
computationally intractable to localize adversarial errors. 2. New network
coding schemes are designed that improve the tomographic performance of RLNC
while maintaining the desirable low-complexity, throughput-optimal, distributed
linear network coding properties of RLNC. In particular, we design network
codes based on Reed-Solomon codes so that a maximal number of adversarial
errors can be localized in a computationally efficient manner even without the
information of network topology.Comment: 40 pages, under submission for IEEE Trans. on Information Theor
