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.
Highlights
This work studies the energy-distortion tradeoff (EDT) for the transmission of a pair of correlatedGaussian sources over a two-user Gaussian broadcast channel (GBC) with noiseless, causal feedback, referred to as the GBCF
We first consider the case of fixed signal-to-noise ratio (SNR) and derive an upper bound on the number of channel uses required to achieve a target distortion pair
We studied the EDT for sending correlated Gaussian sources over GBCFs, without constraining the source-channel bandwidth ratio
Summary
This work studies the energy-distortion tradeoff (EDT) for the transmission of a pair of correlatedGaussian sources over a two-user Gaussian broadcast channel (GBC) with noiseless, causal feedback, referred to as the GBCF. The EDT was originally proposed in [1] to characterize the minimum energy-per-source sample required to achieve a target distortion at the receiver, without constraining the source-channel bandwidth ratio. In various emerging applications, in the context of the Internet of Things, the sampling rates are low; and the channel bandwidth for transmission is much larger than the rate of the sources. In wireless body-area sensor networks, wireless computing devices located on, or inside, the human body measure physiological parameters, which typically exhibit correlations as they originate from the same source. These devices commonly have limited energy supply due to Entropy 2017, 19, 243; doi:10.3390/e19060243 www.mdpi.com/journal/entropy
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