The capacity of a class of 3-receiver broadcast channels with degraded message sets

Körner and Marton established the capacity region for the 2-receiver broadcast channel with degraded message sets. Recent results and conjectures suggest that a straightforward extension of the Körner-Marton region to more than 2 receivers is optimal. This paper shows that this is not the case. We establish the capacity region for a class of 3-receiver broadcast channels with 2 degraded message sets and show that it can be strictly larger than the straightforward extension of the Körner-Marton region. The key new idea is indirect decoding, whereby a receiver who cannot directly decode a cloud center, finds it indirectly by decoding satellite codewords. This idea is then used to establish new inner and outer bounds on the capacity region of the general 3-receiver broadcast channel with 2 and 3 degraded message sets. We show that these bounds are tight for some nontrivial cases. The results suggest that the capacity of the 3-receiver broadcast channel with degraded message sets is as at least as hard to find as the capacity of the general 2-receiver broadcast channel with common and private message.