Code at the Receiver, Decode at the Sender: GRAND with Feedback

In a setting where the forward and feedback channel are noisy BSCs, we show how capacity is nearly achievable in a scheme with only source coding on the forward channel. In representative settings with noisy feedback, GRAND makes the scheme not only possible but practical. The sender transmits uncoded messages, and the receiver provides a noise effect guess as in GRAND, which is channel-encoded and sent to the receiver. With noiseless, finite-length feedback our scheme provides the type of super exponential error behavior associated in previous work with infinite-capacity feedback channels. With noisy feed-back, which is the more common setting in most systems, our scheme permits forward throughput that is effectively the same as in a noiseless feedback case. Moreover, the feedback channel usage remains limited. We propose a target error rate as a useful design parameter.