Attainable error exponents for the Poisson broadcast channel with degraded message sets

The Poisson broadcast channel with degraded message sets models a bandwidth unlimited optical broadcast network over which a sender communicates a common message to a pair of terminals and a private message to just one of them. The capacity region for this communication model is determined by the Körner-Marton result, which in the Poisson regime is shown to coincide with the capacity region of the degraded broadcast channel. We present explicit code construction and practical decoding rules which attain the corresponding capacity region, while attempting to maximize the attainable error exponents at the distinct terminals.