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Joint source-channel coding for a quantum multiple access channel

Mark M. Wilde, Ivan Savov

Published Jan 1, 2012• 3 citations
OpenAlex

Abstract

Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler separation strategy where separate codebooks are used for the source coding and the channel coding tasks. In this paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold. © 2012 IOP Publishing Ltd.

Related papers

Joint source–channel coding for a quantum multiple access channel

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Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal and Salehi provided a combined source–channel coding strategy for a classical multiple access channel which outperforms the simpler ‘separation’ strategy where separate codebooks are used for the source coding and the channel coding tasks. In this paper, we prove that a coding strategy similar to the Cover–El Gamal–Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.

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Unified approach for computing sum of sources over CQ-MAC

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We consider the task of communicating a generic bivariate function of two classical 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. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

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Computing Sum of Sources Over a Classical-Quantum MAC

Mohammad Aamir Sohail, Touheed Anwar Atif, Arun Padakandla +1 more

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.

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We prove coding theorems for two scenarios of cooperating encoders for the multiple access channel with two classical inputs and one quantum output. In the first scenario (ccq-MAC with common message), the two senders each have their private messages, but would also like to transmit common messages. In the second scenario (ccq-MAC with conferencing encoders), each sender has its own set of messages, but they are allowed to use a limited amount of noiseless classical communication amongst each other prior to encoding their messages. This conferencing protocol may depend on each individual message they intend to send. The two scenarios are related to each other not only in spirit - the existence of a capacity-achieving construction scheme for codes for the ccq-MAC with common messages is used for proving the existence of another such scheme for the ccq-MAC with conferencing encoders.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•1 citation

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arXiv:2103.02082•IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•5 citations

One-shot inner bounds for quantum multiple-access one-time pad

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We consider the one-shot coding of multiple access channels one-time pad. Suppose that the senders and the receiver share an entangled state in the multi-party systems. Using the position-based coding, each sender encodes the classical messages on their systems, then they transmit their systems over the ideal quantum channels. The receiver applies a decoding operator to all the systems in order to figure out which message was transmitted with respect to the quantum joint typicality lemma. We provide the upper bound of the information leakage by the convex split lemma. Combining quantum max-information with quantum hypothesis testing mutual information, we give the inner bound of the achievable rate.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Feb 27, 2025•0 citations
Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler separation strategy where separate codebooks are used for the source coding and the channel coding tasks. In this paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold. © 2012 IOP Publishing Ltd.
Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal and Salehi provided a combined source–channel coding strategy for a classical multiple access channel which outperforms the simpler ‘separation’ strategy where separate codebooks are used for the source coding and the channel coding tasks. In this paper, we prove that a coding strategy similar to the Cover–El Gamal–Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.
We consider the task of communicating a generic bivariate function of two classical 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. Inspired by the techniques developed for the classical setting, and employing the technique of simultaneous (joint) decoding developed for the CQ setup, we propose and analyze a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes, and the idea of embedding functions on a prime field. We derive a new set of sufficient conditions that strictly enlarge the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.
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 prove coding theorems for two scenarios of cooperating encoders for the multiple access channel with two classical inputs and one quantum output. In the first scenario (ccq-MAC with common message), the two senders each have their private messages, but would also like to transmit common messages. In the second scenario (ccq-MAC with conferencing encoders), each sender has its own set of messages, but they are allowed to use a limited amount of noiseless classical communication amongst each other prior to encoding their messages. This conferencing protocol may depend on each individual message they intend to send. The two scenarios are related to each other not only in spirit - the existence of a capacity-achieving construction scheme for codes for the ccq-MAC with common messages is used for proving the existence of another such scheme for the ccq-MAC with conferencing encoders.
We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.
We consider the one-shot coding of multiple access channels one-time pad. Suppose that the senders and the receiver share an entangled state in the multi-party systems. Using the position-based coding, each sender encodes the classical messages on their systems, then they transmit their systems over the ideal quantum channels. The receiver applies a decoding operator to all the systems in order to figure out which message was transmitted with respect to the quantum joint typicality lemma. We provide the upper bound of the information leakage by the convex split lemma. Combining quantum max-information with quantum hypothesis testing mutual information, we give the inner bound of the achievable rate.