Coding for the Gaussian Relay Channel with Noisy Feedback

Previously, it has been shown that more feedback links may help to achieve larger finite blocklength rates of the Gaussian relay channel (GRC). However, this is only built on the idealistic assumption that the feedback channels are noise free. In this paper, we revisit the GRC with feedback by considering the situation that the feedback channels are also corrupted by additive white Gaussian noises. For given coding blocklength and decoding error probability, achievable rates of our proposed schemes are characterized. Numerical results show that comparing with those schemes of the same model without using feedback, there may still exist rate gain even the feedback channels are corrupted by noises. Besides this, we also show that comparing with the existing feedback scheme for the GRC with one noise-free feedback link, two noisy feedback links still bring rate gain for some cases.