  We consider a continuous-time bandlimited additive white Gaussian noise
channel with 1-bit output quantization. On such a channel the information is
carried by the temporal distances of the zero-crossings of the transmit signal.
The set of input signals is constrained by the bandwidth of the channel and an
average power constraint. We derive a lower bound on the capacity by
lower-bounding the mutual information rate for a given set of waveforms with
exponentially distributed zero-crossing distances, where we focus on the
behavior in the mid to high signal-to-noise ratio regime. We find that in case
the input randomness scales appropriately with the available bandwidth, the
mutual information rate grows linearly with the channel bandwidth for constant
signal-to-noise ratios. Furthermore, for a given bandwidth the lower bound
saturates with the signal-to-noise ratio growing to infinity. The ratio between
the lower bound on the mutual information rate and the capacity of the additive
white Gaussian noise channel without quantization is a constant independent of
the channel bandwidth for an appropriately chosen randomness of the channel
input and a given signal-to-noise ratio. We complement those findings with an
upper bound on the mutual information rate for the specific signaling scheme.
We show that both bounds are close in the mid to high SNR domain.
