Lattices over Eisenstein Integers for Compute-and-Forward

Nihat Engin Tunali*, Krishna R. Narayanan, Joseph J. Boutros, Yu-Chih Huang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 Scopus citations

Abstract

We consider the use of lattice codes over Eisenstein integers for implementing a compute-and-forward protocol in wireless networks when channel state information is not available at the transmitter. We prove the existence of a sequence of infinite-dimensional nested lattices over Eisenstein integers where the coarse lattice is simultaneously good for quantization and additive white Gaussian noise (AWGN) channel coding and the fine lattice is good for AWGN channel coding. Using this, we show that the information rates achievable with nested lattice codebooks over Eisenstein integers can be higher than those achievable with nested lattices over integers considered by Nazer and Gastpar in [1] for some set of channel realizations. We also propose a practical coding scheme based on the concatenation of a non-binary low density parity check code with a modulation scheme derived from the ring of Eisenstein integers.

Original languageEnglish
Title of host publication2012 50TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON)
PublisherIEEE
Pages33-40
Number of pages8
ISBN (Print)978-1-4673-4537-8
DOIs
StatePublished - 1 Oct 2012
Event50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) - Monticello, Israel
Duration: 1 Oct 20125 Oct 2012

Publication series

NameAnnual Allerton Conference on Communication Control and Computing
PublisherIEEE
ISSN (Print)2474-0195

Conference

Conference50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
CountryIsrael
CityMonticello
Period1/10/125/10/12

Keywords

  • Compute-and-Forward
  • Lattice codes
  • Eisenstein integers
  • CODES

Cite this

Tunali, N. E., Narayanan, K. R., Boutros, J. J., & Huang, Y-C. (2012). Lattices over Eisenstein Integers for Compute-and-Forward. In 2012 50TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON) (pp. 33-40). (Annual Allerton Conference on Communication Control and Computing). IEEE. https://doi.org/10.1109/Allerton.2012.6483196