Lattices over Eisenstein Integers for Compute-and-Forward

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

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In this paper, 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 extend the compute-and-forward paradigm of Nazer and Gastpar to decoding Eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over Eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the Poltyrev limit. Using this result, we show that both the outage performance and error-correcting performance of the nested lattice codebooks over Eisenstein integers surpass those of lattice codebooks over integers considered by Nazer and Gastpar with no additional computational complexity.

Original languageEnglish
Article number7154472
Pages (from-to)5306-5321
Number of pages16
JournalIEEE Transactions on Information Theory
Volume61
Issue number10
DOIs
Publication statusPublished - 1 Oct 2015

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Channel state information
Outages
Decoding
Transmitters
Computational complexity
Wireless networks
Network protocols
performance
paradigm

Keywords

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

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

Lattices over Eisenstein Integers for Compute-and-Forward. / Tunali, Nihat Engin; Huang, Yu Chih; Boutros, Joseph; Narayanan, Krishna R.

In: IEEE Transactions on Information Theory, Vol. 61, No. 10, 7154472, 01.10.2015, p. 5306-5321.

Research output: Contribution to journalArticle

Tunali, Nihat Engin ; Huang, Yu Chih ; Boutros, Joseph ; Narayanan, Krishna R. / Lattices over Eisenstein Integers for Compute-and-Forward. In: IEEE Transactions on Information Theory. 2015 ; Vol. 61, No. 10. pp. 5306-5321.
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