Combined Shaping and 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 PX/PZ ≈ 1 and below. We consider multi-dimensional precoding, with anticipation of Ns > 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 inter-symbol interference channels with Euclidean distance decoder. However, the standard configuration of this scheme does not support precoding at low SNR, where the capacity is less than 1 bit dim . We propose a low rate precoding scheme which combines MMSE estimation, dithering and a variant of nested codes, based on concatenation of a “syndrome dilution” code and a “syndrome-to-coset” modulation code. We provide simulation results for several configurations of nested trellis codes, which reduce the gap to capacity.