  In this paper, we investigate secure transmission over the large-scale
multiple-antenna wiretap channel with finite alphabet inputs. First, we
investigate the case where instantaneous channel state information (CSI) of the
eavesdropper is known at the transmitter. We show analytically that a
generalized singular value decomposition (GSVD) based design, which is optimal
for Gaussian inputs, may exhibit a severe performance loss for finite alphabet
inputs in the high signal-to-noise ratio (SNR) regime. In light of this, we
propose a novel Per-Group-GSVD (PG-GSVD) design which can effectively
compensate the performance loss caused by the GSVD design. More importantly,
the computational complexity of the PG-GSVD design is by orders of magnitude
lower than that of the existing design for finite alphabet inputs in [1] while
the resulting performance loss is minimal. Then, we extend the PG-GSVD design
to the case where only statistical CSI of the eavesdropper is available at the
transmitter. Numerical results indicate that the proposed PG-GSVD design can be
efficiently implemented in large-scale multiple-antenna systems and achieves
significant performance gains compared to the GSVD design.
