Capacity-Approaching Signal Constellations for the Additive Exponential Noise Channel

Abstract: 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.