  The dirty paper channel (DPC) under a peak amplitude constraint arises in an
optical wireless broadcast channel (BC), where the state at one receiver is the
transmitted signal intended for the other receiver(s). This paper studies a
class of peak-constrained DPC that is applicable to the optical wireless BC,
where the channel state (i.e, `dirt') takes values from some evenly-spaced
grid. For the discrete-state DPC studied this paper, a capacity upper bound is
obtained from its state-free counterpart. To lower bound its capacity,
classical dirty paper coding schemes are revisited, including Costa's coding
for DPC and Tomlinson-Harashima (TH) precoding, which serves as benchmark
schemes. To improve the benchmark performance, two new precoding schemes are
proposed for the discrete-state DPC. Although the proposed schemes do not
achieve the state-free capacity contrary to what is known about the Costa's
DPC, achievable rates within a small gap to the state-free capacity are
demonstrated for the discrete-state DPC. Using the proposed precoding scheme in
a two-user peak-constrained Gaussian BC, a new capacity inner bound (IB) is
obtained, and is shown to outperform the truncated Gaussian (TG) based IB and
is comparable to the best-known IB.
