Energy-distortion tradeoff for the gaussian broadcast channel with feedback

IEEE Trans. Inform. Theory

et al. 2017

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Abstract-We study linear encoding for a pair of correlated Gaussian sources transmitted over a two-user Gaussian broadcast channel in the presence of unit-delay noiseless feedback, abbreviated as the GBCF. Each pair of source samples is transmitted using a linear transmission scheme in a finite number of channel uses. We investigate three linear transmission schemes: A scheme based on the Ozarow-Leung (OL) code, a scheme based on the linear quadratic Gaussian (LQG) code of Ardestanizadeh et al., and a novel scheme derived in this work using a dynamic programming (DP) approach. For the OL and LQG schemes we present lower and upper bounds on the minimal number of channel uses needed to achieve a target mean-square error (MSE) pair. For the LQG scheme in the symmetric setting, we identify the optimal scaling of the sources, which results in a significant improvement of its finite horizon performance, and, in addition, characterize the (exact) minimal number of channel uses required to achieve a target MSE. Finally, for the symmetric setting, we show that for any fixed and finite number of channel uses, the DP scheme achieves an MSE lower than the MSE achieved by either the LQG or the OL schemes.

Section: A Prior Workmentioning

confidence: 99%

Finite-Length Linear Schemes for Joint Source-Channel Coding over Gaussian Broadcast Channels with Feedback

IEEE Trans. Inform. Theory

et al. 2017

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“…, and at the IEEE International Symposium on Information Theory (ISIT), July 2016, Barcelona, Spain [47].…”

mentioning

confidence: 99%

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

et al. 2017

Entropy

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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.

Energy-distortion tradeoff for the gaussian broadcast channel with feedback

2016 IEEE International Symposium on Information Theory (ISIT)

et al. 2016

Abstract-This work focuses on the minimum transmission energy required for communicating a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless and causal channel output feedback (GBCF). We study the fundamental limit on the required transmission energy 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. We derive a lower bound and three distinct upper bounds on the minimum required energy. For the upper bounds we analyze three transmission schemes: Two schemes are based on separate source-channel coding, and apply coding over multiple samples of source pairs. The third scheme is based on joint source-channel coding obtained by extending the Ozarow-Leung (OL) transmission scheme, which applies uncoded linear transmission. Numerical simulations show that despite its simplicity, the energy-distortion tradeoff of the OL-based scheme is close to that of the better separation-based scheme, which indicates that the OL scheme is attractive for energy-efficient source transmission over GBCFs. I. INTRODUCTIONWe study the energy-distortion tradeoff (EDT) for the transmission of a correlated pair of Gaussian sources over a twouser Gaussian broadcast channel (GBC) with noiseless causal feedback, referred to as the GBCF. EDT, recently proposed for the multiple-access channel (MAC) and the point-to-point channel in [1], characterizes the minimum energy-per-source sample required to achieve a target distortion pair at the receivers, without constraining the source-channel bandwidth ratio. In many practical scenarios, e.g., satellite broadcasting [2], sensor networks measuring physical processes [3], and in particular wireless body-area sensor networks [4], an extremely high energy efficiency is required for broadcasting correlated observations, while the available power is limited. It follows that there is a strong motivation for studying the EDT for broadcasting correlated sources, and in the present work we focus on EDT for feedback-assisted scenarios, represented by the GBCF.It is well known that, for lossy source transmission over memoryless Gaussian point-to-point channels, with or without feedback, when the bandwidth ratio is fixed and the average power per channel use is limited, separate source and channel coding (SSCC) achieves the minimum possible average distortion [5, Thm. 3]. In [1, Cor. 1] it is further shown that SSCC is optimal in the EDT sense as well: For any target distortion level, the minimal transmission energy is achieved by optimal lossy compression followed by the most energy efficient channel coding.