We present a communication scheme using guessing random additive noise decoding (GRAND) to improve flexibility and reliability of the existing compressed error (CE) framework. The CE framework uses information feedback to construct follow-up transmissions by compressing previous noise realizations, offering high reliability at a code rate close to the forward channel capacity. The channel decoding algorithm GRAND allows us to efficiently maintain this performance in noisy feedback settings by shifting redundancy for forward message protection to the feedback channel. Our scheme, GRAND-CE, is therefore appropriate for cases where forward and feedback channel usage costs are asymmetric, e.g. uplink communications. GRAND-CE offers super-exponential error rate performance as channel use increases, with finite usage of a noisy feedback channel. Unlike the traditional forward error correction model, the receiver performs error correction encoding and the sender handles decoding. We also propose a technique for pipelining sequential transmissions to maintain fixed forward transmission length and good feedback channel coding performance.

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.