AWGNGoodness is Enough: CapacityAchieving Lattice Codes based on Dithered Probabilistic Shaping
Abstract
In this paper we show that any sequence of infinite lattice constellations which is good for the unconstrained Gaussian channel can be shaped into a capacityachieving sequence of codes for the powerconstrained Gaussian channel under lattice decoding and nonuniform signalling. Unlike previous results in the literature, our scheme holds with no extra condition on the lattices (e.g. quantizationgoodness or vanishing flatness factor), thus establishing a direct implication between AWGNgoodness, in the sense of Poltyrev, and capacityachieving codes. Our analysis uses properties of the discrete Gaussian distribution in order to obtain precise bounds on the probability of error and achievable rates. In particular, we obtain a simple characterization of the finiteblocklength behavior of the scheme, showing that it approaches the optimal dispersion coefficient for \textit{high} signaltonoise ratio. We further show that for \textit{low} signaltonoise ratio the discrete Gaussian over centered lattice constellations can not achieve capacity, and thus a shift (or "dither") is essentially necessary.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 arXiv:
 arXiv:1707.06688
 Bibcode:
 2017arXiv170706688C
 Keywords:

 Computer Science  Information Theory
 EPrint:
 20 pages, 2 figures  added two sections (IVC and IVD) on finite dithers and reduced peak power