A Tight Converse to the Asymptotic Performance of Byzantine Distributed Sequential Change Detection

The Byzantine distributed sequential change detection (BDSCD) problem is studied, where a fusion center monitors an abrupt event occurring at an unknown time through a bunch of distributed sensors. It is assume that a part of the sensors are compromised and each sensor, honest or compromised, communicates with the fusion center via a noiseless link. A new converse for this problem is presented whose first-order asymptotic delay subject to a certain false alarm rate coincides with the currently best known result achieved by the consensus rule proposed by Fellouris et al. This result characterizes the first-order asymptotic performance of BDSCD and shows that 1-bit links suffice to achieve the asymptotic optimality. The proof of the converse involves constructing an attack strategy, called the reverse attack, introducing a genie that gives the fusion center the identities of a subset of honest sensors and observations at each sensor used for generating its local report, and transforming the problem into an equivalent non-Byzantine sequential change detection but with reduced number of honest sensors.