  This paper studies the capacity of the peak-and-average-power-limited
Gaussian channel when its output is quantized using a dithered, infinite-level,
uniform quantizer of step size $\Delta$. It is shown that the capacity of this
channel tends to that of the unquantized Gaussian channel when $\Delta$ tends
to zero, and it tends to zero when $\Delta$ tends to infinity. In the low
signal-to-noise ratio (SNR) regime, it is shown that, when the peak-power
constraint is absent, the low-SNR asymptotic capacity is equal to that of the
unquantized channel irrespective of $\Delta$. Furthermore, an expression for
the low-SNR asymptotic capacity for finite peak-to-average-power ratios is
given and evaluated in the low- and high-resolution limit. It is demonstrated
that, in this case, the low-SNR asymptotic capacity converges to that of the
unquantized channel when $\Delta$ tends to zero, and it tends to zero when
$\Delta$ tends to infinity. Comparing these results with achievability results
for (undithered) 1-bit quantization, it is observed that the dither reduces
capacity in the low-precision limit, and it reduces the low-SNR asymptotic
capacity unless the peak-to-average-power ratio is unbounded.
