Construction $\pi_A$ and $\pi_D$ Lattices: Construction, Goodness, and Decoding Algorithms
Abstract
A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of linear codes over , respectively, and hence is referred to as Construction . The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction lattices is proposed and its achievable rate for the additive white Gaussian channel is analyzed. A generalization named Construction is also investigated which subsumes Construction A with codes over prime fields, Construction D, and Construction as special cases.
Keywords
Cite
@article{arxiv.1506.08269,
title = {Construction $\pi_A$ and $\pi_D$ Lattices: Construction, Goodness, and Decoding Algorithms},
author = {Yu-Chih Huang and Krishna R. Narayanan},
journal= {arXiv preprint arXiv:1506.08269},
year = {2017}
}
Comments
26 pages, 11 figures. arXiv admin note: text overlap with arXiv:1401.2228