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We consider the scenario of communicating on a $3\mhyphen$userclassical-quantum broadcast channel. We undertake an information theoreticstudy and focus on the problem of characterizing an inner bound to its capacityregion. We design a new coding scheme based \textit{partitioned coset codes} -an ensemble of codes possessing algebraic properties. Analyzing itsinformation-theoretic performance, we characterize a new inner bound. Weidentify examples for which the derived inner bound is strictly larger thanthat achievable using IID random codes.

An Achievable Rate Region for $3-$User Classical-Quantum Broadcast Channels