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We study a two-user state-dependent generalized multiple-access channel(GMAC) with correlated states. It is assumed that each encoder has\emph{noncausal} access to channel state information (CSI). We develop anachievable rate region by employing rate-splitting, block Markov encoding,Gelfand--Pinsker multicoding, superposition coding and joint typicalitydecoding. In the proposed scheme, the encoders use a partial decoding strategyto collaborate in the next block, and the receiver uses a backward decodingstrategy with joint unique decoding at each stage. Our achievable rate regionincludes several previously known regions proposed in the literature fordifferent scenarios of multiple-access and relay channels. Then, we considertwo Gaussian GMACs with additive interference. In the first model, we assumethat the interference is known noncausally at both of the encoders andconstruct a multi-layer Costa precoding scheme that removes \emph{completely}the effect of the interference. In the second model, we consider a doubly dirtyGaussian GMAC in which each of interferences is known noncausally only at oneencoder. We derive an inner bound and analyze the achievable rate region forthe latter model and interestingly prove that if one of the encoders knows thefull CSI, there exists an achievable rate region which is \emph{independent} ofthe power of interference.

Multi layer Gelfand Pinsker Strategies for the Generalized Multiple Access Channel