  We present a new family of signal constellations, called log constellations,
that can be used to design near-capacity coded modulation schemes over additive
exponential noise (AEN) channels. Log constellations are designed by
geometrically approximating the input distribution that maximizes the AEN
channel capacity. The mutual information achievable over AEN channels with both
coded modulation (CM) and bit-interleaved coded modulation (BICM) approaches is
evaluated for various signal sets. In the case of CM, the proposed log
constellations outperform, sometimes by over half a decibel, the best existing
signal sets available from the literature, and can display error performance
within only 0.12 dB of the AEN channel capacity. In the context of BICM, log
constellations do not offer significant performance advantages over the best
existing constellations. As the potential performance degradation resulting
from the use of BICM instead of CM is larger than 1 dB, BICM may however not be
a suitable design approach over AEN channels.
