  This work contains two single-letter upper bounds on the entropy rate of a
discrete-valued stationary stochastic process, which only depend on
second-order statistics, and are primarily suitable for models which consist of
relatively large alphabets. The first bound stems from Gaussian maximum-entropy
considerations and depends on the power spectral density (PSD) function of the
process. While the PSD function cannot always be calculated in a closed-form,
we also propose a second bound, which merely relies on some finite collection
of auto-covariance values of the process. Both of the bounds consist of a
one-dimensional integral, while the second bound also consists of a
minimization problem over a bounded region, hence they can be efficiently
calculated numerically. Examples are also provided to show that the new bounds
outperform the standard conditional entropy bound.
