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

TL;DR

This paper introduces a new coding scheme using partitioned coset codes for 3-user classical-quantum broadcast channels, achieving larger inner bounds on capacity regions than previous methods.

Contribution

It develops a novel algebraic coding scheme and combines it with advanced decoding techniques to improve the achievable rate region for 3-user classical-quantum broadcast channels.

Findings

New inner bound surpasses previous bounds with IID codes

Partitioned coset codes improve capacity region estimates

Enhanced decoding via Sen's tilting technique

Abstract

We consider the scenario of communicating on a $3\mhyphen$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 \textit{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.