Short-Packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback

We present an upper bound on the error probability achievable using variable-length stop feedback (VLSF) codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. Numerical evaluation of our bound suggests that, for fixed latency and reliability constraints, noise in the feedback link may increase the minimum average service time for the VLSF scheme considered in this paper, to the extent that fixed-length codes without feedback may be preferable in some scenarios.