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arXiv:2203.00110

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

Gouiaa, Fatma, Padakandla, Arun

Published Feb 28, 2022• 0 citations
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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.

DOI
10.48550/arxiv.2203.00110

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We consider the scenario of communicating on a 3-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 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.
We undertake a Shannon theoretic study of the problem of communicating bit streams over a 3-user classical-quantum interference channel (3-CQIC) and focus on characterizing inner bounds. We design a new coding strategy based on (i) coset codes possessing algebraic closure properties and (ii) decoding POVMs to decode bi-variate interference efficiently. Needing to perform simultaneous decoding, we enhance Sen's powerful technique of tilting, smoothing, and augmentation - originally designed only for IID codes - to decode into `functions of codebooks'. Developing analysis techniques to combine all of these elements, we derive a new inner bound to the capacity region of a 3-CQIC. The derived inner bound subsumes all currently known inner bounds and is analytically proven to be strictly larger for identified examples, including non-commutative `additive' and `non-additive' ones.
We consider the problem of characterizing an inner bound to the capacity region of a 3—user classical-quantum interference channel (3—CQIC). The best known coding scheme for communicating over CQICs is based on unstructured random codes and employs the techniques of message splitting and superposition coding. For classical 3—user interference channels (ICs), it has been proven that coding techniques based on coset codes - codes possessing algebraic closure properties - strictly outperform all coding techniques based on unstructured codes. In this work, we develop analogous techniques based on coset codes for 3to1—CQICs - a subclass of 3—user CQICs. We analyze its performance and derive a new inner bound to the capacity region of 3to1—CQICs that subsume the current known largest and strictly enlarges the same for identified examples.
We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with classical state information non-causally available at the transmitters, henceforth referred to as a QMSTx. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on union coset codes - codes possessing algebraic closure properties and derive a new inner bound that subsumes the largest known inner bound based on IID random coding. We identify examples for which the derived inner bound is strictly larger.
We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with random classical states non-causally available at the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple access analogue of the channel considered by Gelfand and Pinsker in 1980. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on \textit{union coset codes} - codes possessing algebraic properties and derive a new inner bound that subsumes the inner based on IID random coding. We identify examples for which the derived inner bound is strictly larger.