On the transmission of a bivariate Gaussian source over the Gaussian broadcast channel with feedback

We study the uncoded transmission of a bivariate Gaussian source over a two-user symmetric Gaussian broadcast channel with a unit-delay noiseless feedback (GBCF), assuming that each (uncoded) source sample is transmitted using a finite number of channel uses, and that the transmission scheme is linear. We consider three transmission schemes: The scheme of Ardestanizadeh et al., which is based on linear quadratic Gaussian (LQG) control theory, the scheme of Ozarow and Leung (OL), and a novel scheme derived in this work designed using a dynamic programing (DP) approach. For the LQG scheme we characterize the minimal number of channel uses needed to achieve a specified mean-square error (MSE). For the OL scheme we present lower and upper bounds on the minimal number of channel uses needed to achieve a specified MSE, which become tight when the signal-to-noise ratio approaches zero. Finally, we show that for any fixed and finite number of channel uses, the proposed DP scheme achieves MSE lower than the MSE achieved by either the LQG or the OL schemes.