Achieving the Dirty Paper Channel Capacity With Scalar Lattices and Probabilistic Shaping

Reliable communication rates are derived for a dirty paper coding scheme with scalar lattices and probabilistic shaping. The scheme is shown to achieve the capacity of additive white Gaussian noise (AWGN) channels with additive interference. Rate bounds are computed as a function of the block length under the simplifying assumption of perfect constellation shaping. A normal approximation (NA) for the rates approaches a NA for standard AWGN channels at high signal-to-noise ratio (SNR), but the interference degrades performance at low SNR.