Multi-layer Gelfand-Pinsker strategies for the generalized multiple-access channel

We study a two-user state-dependent generalized multiple-access channel (GMAC) with correlated states. It is assumed that each encoder noncausally knows partial channel state information. We develop an achievable rate region by employing rate-splitting, block Markov encoding, Gelfand-Pinsker multicoding, superposition coding and jointly typical 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 a joint unique decoding at each stage. Our achievable rate region includes several previously known rate regions proposed in the literature for different scenarios of multiple-access and relay channels. We finally consider a Gaussian GMAC with an additive interference which is known noncausally at both of the encoders and construct a multi-layer Costa precoding scheme that removes completely the effect of the interference.