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IEEE International Symposium on Information Theory (ISIT)

Communicating Over a Classical-Quantum MAC With State Information Distributed at the Senders

Arun Padakandla

Published Jun 26, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1109/isit50566.2022.9834510

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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.
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.
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.
An Achievable Rate Region for 3−3-3−User Classical-Quantum Broadcast Channels
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 3−3-3−user classical-quantum broadcast channel. Finally, in our last step, we characterize a new inner bound to the classical-quantum capacity region of the 3−3-3−user classical-quantum broadcast channel that subsumes all previous known inner bounds by combining the conventional unstructured IID codes with structured coset code strategies.
We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.
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.