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

TL;DR

This paper derives an upper bound on error probability for variable-length stop feedback codes over noisy feedback channels, highlighting the impact of feedback noise on latency and reliability in short-packet transmissions.

Contribution

It extends existing bounds to noisy feedback scenarios, providing a more realistic analysis of short-packet communication systems with variable-length codes.

Findings

Feedback noise increases minimum average service time.

Noisy feedback can make fixed-length codes preferable.

The bound applies to practical noisy feedback conditions.

Abstract

We present an upper bound on the error probability achievable using variable-length stop feedback 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. By numerically evaluating our bound, we illustrate that, for fixed latency and reliability constraints, noise in the feedback link can cause a significant increase in the minimum average service time, to the extent that fixed-length codes without feedback may be preferable in some scenarios.