Design of Polar Code Lattices of Small Dimension
Information Theory
2021-02-09 v1 math.IT
Abstract
Polar code lattices are formed from binary polar codes using Construction D. In this paper, we propose a design technique for finite-dimension polar code lattices. The dimension and target probability of decoding error are parameters for this design. To select the rates of the Construction D component codes, rather than using the capacity as in past work, we use the explicit finite-length properties of the polar code. Under successive cancellation decoding, density evolution allows choosing code rates that satisfy the equal error probability rule. At an error-rate of , a dimension polar code lattice achieves a VNR of 2.5 dB, within 0.2 dB of the best-known BCH code lattice, but with significantly lower decoding complexity.
Keywords
Cite
@article{arxiv.2102.03998,
title = {Design of Polar Code Lattices of Small Dimension},
author = {Obed Rhesa Ludwiniananda and Ning Liu and Khoirul Anwar and Brian M. Kurkoski},
journal= {arXiv preprint arXiv:2102.03998},
year = {2021}
}