Lattices Over Eisenstein Integers for Compute-and-Forward Academic Article

abstract

• 2014 IEEE. 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.

authors

• Boutros, Joseph
• Narayanan, Krishna

published proceedings

• IEEE TRANSACTIONS ON INFORMATION THEORY

author list (cited authors)

• Tunali, N. E., Huang, Y., Boutros, J. J., & Narayanan, K. R.

citation count

• 31

complete list of authors

• Tunali, Nihat Engin||Huang, Yu-Chih||Boutros, Joseph J||Narayanan, Krishna R

publication date

• October 2015

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• IEEE TRANSACTIONS ON INFORMATION THEORY  Journal

keywords

• Compute-and-forward
• Eisenstein Integers
• Lattice Codes

Digital Object Identifier (DOI)

• 10.1109/TIT.2015.2451623

start page

• 5306

end page

• 5321

volume

• 61

issue

• 10

URL

• http%3A%2F%2Fdx.doi.org%2F10.1109%2Ftit.2015.2451623