On Achievable Rates of Evenly-Spaced Discrete Uniform Distributions in the IM/DD Broadcast Channel

TL;DR

This paper derives a new, tighter capacity inner bound for peak-constrained Gaussian broadcast channels in optical wireless communications using evenly-spaced discrete uniform distributions, improving understanding of achievable rates.

Contribution

It introduces an analytical capacity inner bound for the peak-constrained Gaussian BC using ESDU, which is more practical and tighter than previous benchmarks.

Findings

The inner bound is easily computable.

Numerical results show the bound is tighter than existing benchmarks.

An analytical upper bound for ESDU rate is also developed and is tight.

Abstract

In optical wireless communications, a broadcast channel (BC) employing intensity modulation and direct detection (IM/DD) is often modelled as a peak-constrained BC. A closed-form expression for its capacity region of the peak-constrained BC is not known. This paper presents an analytical capacity inner bound for the peak-constrained Gaussian BC achieved by a class of discrete input distribution, specifically, the evenly-spaced discrete uniform distribution (ESDU). In contrast to the continuous input distribution that provides the benchmark, ESDU is more promising in the application of peak-constrained Gaussian channels. The newly obtained capacity inner bound is easily-computable and is numerically shown to be tighter than the benchmark. Besides, we remark the newly developed analytical upper bound for the ESDU rate, which is tight in all tested settings.