A characterization of the error exponent for the Byzantine CEO problem

The discrete CEO problem is considered when the agents are under Byzantine attack. That is, a malicious intruder has captured an unknown subset of the agents and reprogrammed them to increase the probability of error. Two traitor models are considered, depending on whether the traitors are able to see honest agents' messages before choosing their own. If they can, bounds are given on the error exponent with respect to the sum-rate as a function of the fraction of agents that are traitors. The number of traitors is assumed to be known to the CEO, but not their identity. If they are not able to see the honest agents' messages, an exact but uncomputable characterization of the error exponent is given. It is shown that for a given sum-rate, the minimum achievable probability of error is within a factor of two of a quantity based on the traitors simulating a false distribution to generate messages they send to the CEO. This false distribution is chosen by the traitors to increase the probability of error as much as possible without revealing their identities to the CEO. Because this quantity is always within a constant factor of the probability of error, it gives the error exponent directly.