Bosonic Dirty Paper Coding

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.