Achievable rate regions for compound multiple access channel with channel state information

We study the two-user discrete memoryless compound multiple access channel (MAC) with common message and two specially correlated channel states each known non-causally by one of the encoders. Two channel states are correlated in the sense of Slepian-Wolf (SW) in which two correlated states are modeled by three independent states: a common state and two private states. By using superposition coding, binning scheme and jointly decoding, we propose several achievable rates for various cases of the two-user compound MAC with non-causal Slepian-Wolf channel states available at encoders and common message or conferencing encoders. Also, we show that the obtained achievable rate regions are optimal when perfect states are known at both decoders as well.