Lattices over Eisenstein Integers for Compute-and-Forward

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

Research output: Contribution to journalArticle

21 Citations (Scopus)


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
Issue number10
Publication statusPublished - 1 Oct 2015



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

ASJC Scopus subject areas

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

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