Capacity bounds for dimmable visible light communications using PIN photodiodes with input-dependent Gaussian noise

In this paper, we focus on a dimmable visible light communication (VLC) system using PIN photodiodes. In such a system, the main distortion is caused by additive Gaussian noise, however, with a noise variance depending on the current signal strength. Under the non-negativity, peak power and dimmable average power constraints, the lower and upper bounds on the channel capacity are derived, respectively. Specifically, the derivation of the lower bound is based on the fact that the entropy of the output is always larger than the entropy of the input, while the derivation of the upper bound relies on the dual expression of the channel capacity and the notion of capacity-achieving input distribution that escape to infinity. Numerical results show that the gap between the lower and upper bounds is very small in the VLC application zone.