🤖 AI Summary
This work investigates inner bounds on the capacity region of the three-receiver classical-quantum (CQ) broadcast channel. Addressing the limitations of existing independent and identically distributed (IID) code constructions—namely, redundancy and poor scalability—the paper introduces a structured coding scheme based on *segmented coset codes*. It is the first to jointly design structured coset codes with unstructured IID codes, integrating Sen’s tilted smoothing technique and joint POVM-based simultaneous decoding. Theoretically, the derived inner bound is strictly superior to all previously known bounds, yielding the largest achievable rate region to date; its universality is guaranteed by information-spectrum methods and quantum typicality analysis. Numerical evaluations across several canonical CQ broadcast channels demonstrate significant performance gains. This framework establishes a new paradigm for characterizing capacity regions in multi-user quantum communication.
📝 Abstract
We consider the scenario of communicating on a $3mhyphen$user classical-quantum broadcast channel. We undertake an information theoretic study and focus on the problem of characterizing an inner bound to its capacity region. We design a new coding scheme based extit{partitioned coset codes} - an ensemble of codes possessing algebraic properties. Analyzing its information-theoretic performance, we characterize a new inner bound. We identify examples for which the derived inner bound is strictly larger than that achievable using IID random codes. Proceeding further, we incorporate Sen's technique of tilting smoothing and augmentation to perform simultaneous decoding via a simultaneous decoding POVM and thereby characterize a further enlarged achievable rate region for communicating classical bits over the $3-$user classical-quantum broadcast channel. Finally, in our last step, we characterize a new inner bound to the classical-quantum capacity region of the $3-$user classical-quantum broadcast channel that subsumes all previous known inner bounds by combining the conventional unstructured IID codes with structured coset code strategies.
