On 3-receiver broadcast channels with 2-degraded message sets

We consider a broadcast channel with 3 receivers and 2 messages (M₀, M₁) where two of the three receivers need to decode messages (M₀, M₁) while the remaining one just needs to decode the message M₀. We study the best known inner and outer bounds under this setting, in an attempt to find the deficiencies with the current techniques of establishing the bounds. We produce a simple example where we are able to explicitly evaluate the inner bound and show that it differs from the general outer bound. For a class of channels where the general inner and outer bounds differ, we use a new argument to show that the inner bound is tight.