  The single-mode bosonic channel is addressed with classical interference in
the modulation and with side information at the transmitter. This model can
viewed as the quantum counterpart of the classical random-parameter Gaussian
channel. Based on Costa's writing-on-dirty-paper result (1983), the effect of
the channel parameter can be canceled even when the decoder has no side
information, and regardless of the input power constraint. For both homodyne
and heterodyne detection with a coherent-state protocol, the model reduces to a
classical channel with either real or complex-valued Gaussian noise. Thereby,
by applying Costa's dirty paper coding strategy, we observe that the effect of
the classical interference can be canceled for those channels as well. Then, we
consider the bosonic channel with joint detection, for which the classical
results do not apply, and derive a dirty-paper coding lower bound. Furthermore,
considering the special case of a pure-loss bosonic channel, we demonstrate
that the optimal coefficient for dirty paper coding is not necessarily the MMSE
estimator coefficient as in the classical setting.
