  Data-driven optimization of transmitters and receivers can reveal new
modulation and detection schemes and enable physical-layer communication over
unknown channels. Previous work has shown that practical implementations of
this approach require a feedback signal from the receiver to the transmitter.
In this paper, we study the impact of quantized feedback in data-driven
learning of physical-layer communication. A novel quantization method is
proposed, which exploits the specific properties of the feedback signal and is
suitable for non-stationary signal distributions. The method is evaluated for
linear and nonlinear channels. Simulation results show that feedback
quantization does not appreciably affect the learning process and can lead to
excellent performance, even with $1$-bit quantization. In addition, it is shown
that learning is surprisingly robust to noisy feedback where random bit flips
are applied to the quantization bits.
