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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 theremaining one just needs to decode the message M0. We study the best knowninner and outer bounds under this setting, in an attempt to find thedeficiencies with the current techniques of establishing the bounds. We producea simple example where we are able to explicitly evaluate the inner bound andshow that it differs from the general outer bound. For a class of channelswhere the general inner and outer bounds differ, we use a new argument to showthat the inner bound is tight.

On the inner and outer bounds of 3-receiver broadcast channels with 2-degraded message sets