English

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 nn 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 10410^{-4}, a dimension n=128n=128 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}
}