Code at the Receiver, Decode at the Sender: Feedback Communication with GRAND-CE

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.