Precoding for interference cancellation at low SNR

We investigate the application of the nested coding framework for cancelling known interference at low SNR, that is P_X/P_Z≈1 and below. We consider multi-dimensional precoding, with anticipation of N_s>1 "future" interference samples. Unlike non-precoded transmission, where capacity can be achieved at low SNR without shaping, optimum precoding at low SNR does require shaping. Eyuboglu and Forney\´s trellis precoding scheme combines Tomlinson-Harashima precoding and trellis shaping, to achieve both coding and shaping gains in transmission over intersymbol interference channel with Euclidean distance decoder. However, the standard configuration of this scheme does not support precoding at low SNR, where the capacity is less than 1bit/dim. Inspired by the nested lattices approach, we propose a variant of trellis precoding which combines MMSE estimation, dithering and construction of nested lattices which approach the interference channel capacity at low SNR.