# On the capacity of bandlimited optical intensity channels with Gaussian noise

## TL;DR

This paper analyzes the capacity limits of bandlimited optical intensity channels with Gaussian noise under various power constraints, providing bounds that characterize high SNR behavior and practical signaling strategies.

## Contribution

It introduces new capacity bounds for BLOIC under different constraints and proposes ISI-free signaling methods that outperform existing bounds at low SNR.

## Key findings

- High SNR capacity characterized within a finite gap.
- DOF-optimal bounds match upper bounds in pre-log factor.
- ISI-free signaling bounds outperform DOF bounds below 10 dB SNR.

## Abstract

We determine lower and upper bounds on the capacity of bandlimited optical intensity channels (BLOIC) with white Gaussian noise. Three types of input power constraints are considered: 1) only an average power constraint, 2) only a peak power constraint, and 3) an average and a peak power constraint. Capacity lower bounds are derived by a two-step process including 1) for each type of constraint, designing admissible pulse amplitude modulated input waveform ensembles, and 2) lower bounding the maximum achievable information rates of the designed input ensembles. Capacity upper bounds are derived by exercising constraint relaxations and utilizing known results on discrete-time optical intensity channels. We obtain degrees-of-freedom-optimal (DOF-optimal) lower bounds which have the same pre-log factor as the upper bounds, thereby characterizing the high SNR capacity of BLOIC to within a finite gap. We further derive intersymbol-interference-free (ISI-free) signaling based lower bounds, which perform well for all practical SNR values. In particular, the ISI-free signaling based lower bounds outperform the DOF-optimal lower bound when the SNR is below 10 dB.