Capacity Bounds for the Einstein Radiation Channel

This paper investigates the transmission of information by placing balls in urns. Alice, the transmitter, encodes her message in her choice of the number of balls at each urn, which follows a Poisson distribution, and is subject to an average constraint. Two adversaries, Marvin and Charlie, also put balls into the urns, respectively with geometric and Poisson distributions. Bob, the receiver, retrieves the message by counting the balls in all urns. We provide upper and lower bounds to the channel capacity. We further illustrate the links between this model and electromagnetic radiation, by replacing balls by photons and urns by frequencies or colours