Constellation constrained capacity of additive Gaussian mixture noise channels

Communication channels that are characterized by additive Gaussian noise have been well studied. However, many practical systems are also known to experience non-Gaussian noise. A convenient method to analyse such systems is by modelling the non-Gaussian noise using Gaussian mixture densities. In this paper we compute the constellation constrained (CC) capacity of additive Gaussian mixture (GM) noise channels with finite input alphabets. We study a wide spectrum of GM densities covering single lobe, multi-lobe, symmetric tapering and asymmetric tapering densities. We show that the CC capacity of GM densities is larger than that of the Gaussian density of the same variance at low SNR values. This observation points at the drawback of the existing capacity achieving codes matched to Gaussian channels, and highlights the need for constructing new codes for such channels. We also study GM noise models with data dependent density parameters, that have been recently shown to approximate the NAND flash memory channels.