Nested trellis codes and shaping for the transmitter side-information problem

In this paper, we specifically focus on the problem of power shaping and we examine nested constructions based on trellis codes, which build on simple low dimensional lattices. We propose the idea of performing shaping through a coarse lattice (source code) and we also show how this method can actually be combined with shaping through a fine lattice (channel code) so that a joint shaping can be performed by the fine and coarse lattices in the communication channel with transmitter side-information simultaneously.