Robust decoding for timing channels

To transmit information by timing arrivals to a single-server queue, we consider using the exponential server channel´s maximum likelihood decoder. For any server with service times that are stationary and ergodic with mean 1/μ seconds, we show that the rate e ^-1μ nats per second (capacity of the exponential server timing channel) is achievable using this decoder. We show that a similar result holds for the timing channel with feedback. We also show that if the server jams communication by adding an arbitrary amount of time to the nominal service time, then the rate e^-1μ₁μ₂/(μ₁+μ ₂) nats per second is achievable with random codes, where the nominal service times are stationary and ergodic with mean 1/μ₁ seconds, and the arithmetic mean of the delays added by the server does not exceed 1/μ₂ seconds. This is a model of an arbitrarily varying channel where the current delay and the current input can affect future outputs. We also show the counterpart of these results for single-server discrete-time queues