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We consider the problem of communicating over a classical-quantum (CQ)multiple access channel with random classical states non-causally available atthe transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multipleaccess analogue of the channel considered by Gelfand and Pinsker in 1980. Weundertake a Shannon-theoretic study and focus on the problem of characterizinginner bounds to the capacity region of a QMSTx. We propose a new coding schemebased on \textit{union coset codes} - codes possessing algebraic properties andderive a new inner bound that subsumes the inner based on IID random coding. Weidentify examples for which the derived inner bound is strictly larger.

Communicating over a Classical-Quantum MAC with State Information Distributed at Senders