  This paper provides new insight into the classical problem of determining
both the capacity of the discrete-time channel with uniform output quantization
and the capacity achieving input distribution. It builds on earlier work by
Gallager and Witsenhausen to provide a detailed analysis of two particular
quantization schemes. The first is saturation quantization where overflows are
mapped to the nearest quantization bin, and the second is wrapping quantization
where overflows are mapped to the nearest quantization bin after reduction by
some modulus. Both the capacity of wrapping quantization and the capacity
achieving input distribution are determined. When the additive noise is
gaussian and relatively small, the capacity of saturation quantization is shown
to be bounded below by that of wrapping quantization. In the limit of
arbitrarily many uniform quantization levels, it is shown that the difference
between the upper and lower bounds on capacity given by Ihara is only 0.26
bits.
