  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 an
achievable rate region by employing rate-splitting, block Markov encoding,
Gelfand--Pinsker multicoding, superposition coding and joint typicality
decoding. In the proposed scheme, the encoders use a partial decoding strategy
to collaborate in the next block, and the receiver uses a backward decoding
strategy with joint unique decoding at each stage. Our achievable rate region
includes several previously known regions proposed in the literature for
different scenarios of multiple-access and relay channels. Then, we consider
two Gaussian GMACs with additive interference. In the first model, we assume
that the interference is known noncausally at both of the encoders and
construct a multi-layer Costa precoding scheme that removes \emph{completely}
the effect of the interference. In the second model, we consider a doubly dirty
Gaussian GMAC in which each of interferences is known noncausally only at one
encoder. We derive an inner bound and analyze the achievable rate region for
the latter model and interestingly prove that if one of the encoders knows the
full CSI, there exists an achievable rate region which is \emph{independent} of
the power of interference.
