  Providing secure communications over the physical layer with the objective of
achieving perfect secrecy without requiring a secret key has been receiving
growing attention within the past decade. The vast majority of the existing
studies in the area of physical layer security focus exclusively on the
scenarios where the channel inputs are Gaussian distributed. However, in
practice, the signals employed for transmission are drawn from discrete signal
constellations such as phase shift keying and quadrature amplitude modulation.
Hence, understanding the impact of the finite-alphabet input constraints and
designing secure transmission schemes under this assumption is a mandatory step
towards a practical implementation of physical layer security. With this
motivation, this article reviews recent developments on physical layer security
with finite-alphabet inputs. We explore transmit signal design algorithms for
single-antenna as well as multi-antenna wiretap channels under different
assumptions on the channel state information at the transmitter. Moreover, we
present a review of the recent results on secure transmission with discrete
signaling for various scenarios including multi-carrier transmission systems,
broadcast channels with confidential messages, cognitive multiple access and
relay networks. Throughout the article, we stress the important behavioral
differences of discrete versus Gaussian inputs in the context of the physical
layer security. We also present an overview of practical code construction over
Gaussian and fading wiretap channels, and we discuss some open problems and
directions for future research.
