Capacity region of the 3 receiver state dependent multilevel BC with noncausal state information

We consider a three receiver state dependent multilevel broadcast channel (BC), where the state information is known non-causally at the encoder as well as all the decoders. This is an extension of Nair and El Gamal's three receiver multilevel BC (Nair and El Gamal, 2009), wherein two of the receivers decode only a common message while a third receiver decodes a private message as well. The objective is to characterize the rate tuples that are simultaneously achievable while ensuring negligible probability of error at each of the receivers. We characterize the capacity region of this setup in the paper.