On rate and BER analysis for finite-dimensional lattice coding for the dirty paper channel

Costa's dirty paper coding (DPC) offers a good framework for precoding for transmission over additive Gaussian channels with additive states non-causally known at the transmitter but not at the receiver. In this paper, rate calculation, error probability analysis and code design for DPC are investigated from a practical point-of-view. Based on Monte-Carlo numerical integration and simulations, we first show that the gap to the full AWGN capacity can be partially bridged using some finite-dimensional lattices with good packing and quantizing properties. Then the difficult problem of codebook selection is addressed through some illustrative examples. Analysis sheds light on the dual roles of “packing” and “shaping” as well as on their inter-connection at finite-dimensional coding, by opposition to the asymptotic case (i.e., infinite dimension) where the two coding components are decoupled.