Superposition coding is almost always optimal for the Poisson broadcast channel

This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal (e.g., degraded, less noisy, more capable). For the rest of the channel parameter values, we show that there is a gap between Marton´s inner bound and the UV outer bound.