Nested trellis codes and shaping for the transmitter side-information problem - Information Theory, 2003. Proceedings. IEEE International Symposium on

where X is the transmit vector signal, Y is the receive vector signal, S is a Gaussian interference vector signal, and 2 is a Gaussian noise vector. The interference signal S is non-causally known at the transmitter but not known at the receiver, and the noise 2 is independent of X and S and it is not known neither at the transmitter nor at the receiver. The transmit signal must satisfy a power constraint, that is, ~ E [ ~ ~ X ~ ~ 2 ] < P. Using random binning arguments, the capacity of this channel is given by’ C = $ log (det(KX + KZ)/de t (KZ)) where K X and K Z are the covariance matrices of X and 2 respectively. Thus, the effect of the interference S is completely eliminated (by utilizing it through the transmitter side-information) and the capacity of this channel is the same as for the gaussian vector channel without any interference S . In [2], a constructive approach for the random binning arguments of [l] was given through the use of nested lattices A‘ /A2 . 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 p r e pose 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 simultaneously.