Jalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan.
2016) have recently proposed a generalization of R\'enyi's information
dimension to stationary stochastic processes by defining the information
dimension rate as the information dimension of $k$ samples divided by $k$ in
the limit as $k\to\infty$. This paper proposes an alternative definition of
information dimension rate as the entropy rate of the uniformly-quantized
stochastic process divided by minus the logarithm of the quantizer step size
$1/m$ in the limit as $m\to\infty$. It is demonstrated that both definitions
are equivalent for stochastic processes that are $\psi^*$-mixing, but may
differ in general. In particular, it is shown that for Gaussian processes with
essentially-bounded power spectral density (PSD), the proposed information
dimension rate equals the Lebesgue measure of the PSD's support. This is in
stark contrast to the information dimension rate proposed by Jalali and Poor,
which is $1$ if the process's PSD is positive on any set with positive Lebesgue
measure, irrespective of its support size.