  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.
