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

The authors study a two-user state-dependent generalised multiple-access channel (GMAC) with correlated states. It is assumed that each encoder has `non-causal´ access to channel state information (CSI). They 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. The author´s achievable rate region includes several previously known regions proposed in the literature for different scenarios of multiple-access and relay channels. Then, they consider two Gaussian GMACs with additive interference. In the first model, they assume that the interference is known non-causally at both of the encoders and construct a multi-layer Costa precoding scheme that removes `completely´ the effect of the interference. In the second model, they consider a doubly dirty Gaussian GMAC in which each of interferences is known non-causally only at one encoder. They derive an inner bound and analyse 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 `independent´ of the power of interference.