Energy-Distortion Tradeoff for the Gaussian Broadcast Channel with Feedback

TL;DR

This paper investigates the minimum energy needed to broadcast correlated Gaussian sources over a two-user Gaussian broadcast channel with feedback, deriving bounds and analyzing schemes to optimize energy-distortion tradeoff.

Contribution

It introduces new bounds on energy requirements and compares separate and joint coding schemes, extending the OL scheme for improved energy efficiency.

Findings

OL-based scheme achieves near-optimal energy-distortion performance

Joint source-channel coding outperforms separate coding in some regimes

OL scheme is simple yet effective for energy-efficient transmission

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.