Abstract
This paper addresses the detection of information flows through a
pair of nodes in a wireless ad hoc network by correlating the
transmission timing of these nodes. The transmission timing is
subject to perturbations such as random delays and reshuffling,
and there may be chaff traffic induced by traffic multiplexing at
intermediate nodes or the active insertion of dummy traffic.
Furthermore, the collection of timing measurements is subject to
capacity constraints. Under the assumption that information flows
satisfy a bounded delay constraint, the paper characterizes the
tradeoff between data collection payload and detection quality.
The detection performance is measured by the maximum amount of
chaff traffic that allows consistent detection. An upper bound on
the maximum amount of chaff is derived by formulating the problem
as a rate-distortion problem. Joint compression and detection
schemes are proposed for detecting information flows with and
without full side-information, respectively. The proposed schemes
are shown to achieve consistent detection in the presence of chaff
traffic of positive rate under arbitrarily small capacity
constraints. The proposed detectors are proved to be optimal for
the corresponding compression schemes, and a comparison of their
performance gives novel insights into the quantizer design.