  We study the capacity of the discrete-time Gaussian channel when its output
is quantized with a one-bit quantizer. We focus on the low signal-to-noise
ratio (SNR) regime, where communication at very low spectral efficiencies takes
place. In this regime a symmetric threshold quantizer is known to reduce
channel capacity by a factor of 2/pi, i.e., to cause an asymptotic power loss
of approximately two decibels. Here it is shown that this power loss can be
avoided by using asymmetric threshold quantizers and asymmetric signaling
constellations. To avoid this power loss, flash-signaling input distributions
are essential. Consequently, one-bit output quantization of the Gaussian
channel reduces spectral efficiency. Threshold quantizers are not only
asymptotically optimal: at every fixed SNR a threshold quantizer maximizes
capacity among all one-bit output quantizers. The picture changes on the
Rayleigh-fading channel. In the noncoherent case a one-bit output quantizer
causes an unavoidable low-SNR asymptotic power loss. In the coherent case,
however, this power loss is avoidable provided that we allow the quantizer to
depend on the fading level.
