  We prove that the ensemble the nested coset codes built on finite fields
achieves the capacity of arbitrary discrete memoryless point-to-point channels.
Exploiting it's algebraic structure, we develop a coding technique for
communication over general discrete multiple access channel with channel state
information distributed 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-symmteric examples for which the proposed achievable rate region is
strictly larger than the one achievable using random unstructured codes.
