Bounds on the achievable rate of noisy feedback Gaussian channels under linear feedback coding scheme

In this paper, we investigate the additive Gaussian noise channel with noisy feedback. We consider the setup of linear coding of the feedback information and Gaussian signaling of the message (i.e. Cover-Pombra Scheme). Then, we derive the upper and lower bounds on the largest achievable rate for this setup. We show that these two bounds can be obtained by solving two convex optimization problems. Finally, we present some simulations and discussion.