An achievable rate region for 3-user classical quantum broadcast channel via coset codes

We undertake a Shannon theoretic study of the problem of communicating statistically independent bit streams over a 3-user classical quantum broadcast channel (3-CQBC) and focus on characterizing inner bounds to its capacity region. We propose a coding strategy based on coset codes possessing algebraic closure properties. Elevating Sen's technique of tilting, smoothing, and augmentation - originally designed only for IID codes - we design new POVMs that can simultaneously decode into a combination of unstructured IID and coset codes to efficiently decode univariate and bivariate interferences respectively. Analyzing the information-theoretic performance of the proposed coding strategy we characterize a new inner bound to the capacity region of the 3-CQBC that subsumes all currently known bounds and is proven to be strictly larger for identified examples.