An Achievable Rate Region Based on Coset Codes for Multiple Access Channel With States

We prove that the ensemble of the nested coset codes built on finite fields achieves the capacity of arbitrary discrete memoryless point-to-point channels. Exploiting its algebraic structure, we develop a coding technique for communication over general discrete multiple access channel with channel state information distributed noncausally at the transmitters. We build an algebraic coding framework for this problem using the ensemble of Abelian group codes and, thereby, derive a new achievable rate region. We identify non-additive and non-symmetric examples for which the proposed achievable rate region is strictly larger than the one achievable using random unstructured codes.