The bosonic channel is addressed with modulation interference and side information at the transmitter. The model can be viewed as the quantum counterpart of the classical random-parameter Gaussian channel. Based on Costa's writing-on-dirty-paper result, the effect of the interference can be canceled. For both homodyne and heterodyne detection, we observe the same phenomenon, as the model reduces to a classical Gaussian channel. 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. We demonstrate that the optimal coefficient for dirty paper coding is not necessarily the MMSE estimator coefficient as in the classical setting.
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