The stochastic-calculus approach to multi-receiver poisson channels

We study two-receiver Poisson channels using tools derived from stochastic calculus. We compute necessary and sufficient conditions under which the continuous-time, continuous-space Poisson channel is less noisy and more capable, which turn out to be distinct from the conditions under which the “sampled” channel is less noisy and more capable. We also determine the capacity region of the more capable Poisson broadcast channel with independent message sets, the more capable Poisson wiretap channel, and the general two-decoder Poisson broadcast channel with degraded message sets.