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Entropy 2017, 19(6), 243; doi:10.3390/e19060243

On the Energy-Distortion Tradeoff of Gaussian Broadcast Channels with Feedback

1
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
2
Goldman Sachs, New York, NY 10282, USA
3
Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Be’er-Sheva 8410501, Israel
4
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK
*
Author to whom correspondence should be addressed.
Received: 25 April 2017 / Revised: 17 May 2017 / Accepted: 19 May 2017 / Published: 24 May 2017
(This article belongs to the Special Issue Network Information Theory)
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Abstract

This work studies the relationship between the energy allocated for transmitting a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless channel output feedback (GBCF) and the resulting distortion at the receivers. Our goal is to characterize the minimum transmission energy required for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. This minimum transmission energy is defined as the energy-distortion tradeoff (EDT). We derive a lower bound and three upper bounds on the optimal EDT. For the upper bounds, we analyze the EDT of three transmission schemes: two schemes are based on separate source-channel coding and apply encoding over multiple samples of source pairs, and the third scheme is a joint source-channel coding scheme that applies uncoded linear transmission on a single source-sample pair and is obtained by extending the Ozarow–Leung (OL) scheme. Numerical simulations show that the EDT of the OL-based scheme is close to that of the better of the two separation-based schemes, which makes the OL scheme attractive for energy-efficient, low-latency and low-complexity source transmission over GBCFs. View Full-Text
Keywords: Gaussian broadcast channel with feedback; correlated sources; joint source-channel coding; energy efficiency; energy-distortion tradeoff Gaussian broadcast channel with feedback; correlated sources; joint source-channel coding; energy efficiency; energy-distortion tradeoff
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Murin, Y.; Kaspi, Y.; Dabora, R.; Gündüz, D. On the Energy-Distortion Tradeoff of Gaussian Broadcast Channels with Feedback. Entropy 2017, 19, 243.

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