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 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.Comment: Submitted to a Transactions on Wireless Communication

Moderate deviation asymptotics for variable-length codes with feedback

We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are \rho-{N} below the channel capacity C , where \rho-{N} is a positive sequence that tends to zero slower than the reciprocal of the square root of the expectation of the (random) blocklength N. This is known as the moderate deviations regime, and we establish the optimal moderate deviations constant. We show that in this scenario, the error probability decays sub-exponentially with speed \exp (-(B/C)N\rho-{N}) , where B is the maximum relative entropy between output distributions of the DMC