Nested lattice codes for arbitrary continuous sources and channels

In this paper, we show that nested lattice codes achieve the capacity of arbitrary continuous channels with or without non-causal state information at the transmitter. We also show that nested lattice codes are optimal for source coding with or without non-causal side information at the receiver for arbitrary continuous sources. We show the optimality of lattice codes for the Gelfand-Pinsker and Wyner-Ziv problems in their most general settings.