On the ergodic rate for compute-and-forward

Amin Sakzad, Emanuele Viterbo, Yi Hong, Joseph Boutros

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

16 Citations (Scopus)

Abstract

A key issue in compute-and-forward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i]n to a line in the n-dimensional complex Euclidean space, within a bounded region around the origin. We then use the complex version of the LLL lattice basis reduction (CLLL) algorithm to provide a reduced complexity suboptimal solution as well as an upper bound to the minimum distance of the lattice point from the line. Using this bound we are able to find a lower bound to the ergodic rate and a union bound estimate on the error performance of a lattice constellation used for lattice network coding. We compare performance of the CLLL with a more complex iterative optimization method as well as with a simple quantized search. Simulations show how CLLL can trade some performance for a lower complexity.

Original languageEnglish
Title of host publication2012 International Symposium on Network Coding, NetCod 2012
PublisherIEEE Computer Society
Pages131-136
Number of pages6
ISBN (Print)9781467318921
Publication statusPublished - 1 Jan 2012
Event2012 International Symposium on Network Coding, NetCod 2012 - Cambridge, MA, United States
Duration: 29 Jun 201230 Jun 2012

Publication series

Name2012 International Symposium on Network Coding, NetCod 2012

Other

Other2012 International Symposium on Network Coding, NetCod 2012
CountryUnited States
CityCambridge, MA
Period29/6/1230/6/12

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Keywords

  • Clll al-gorithm
  • Compute-and-forward
  • Index terms-ergodic rate
  • Quantized error
  • Successive refinement

ASJC Scopus subject areas

  • Computer Networks and Communications

Cite this

Sakzad, A., Viterbo, E., Hong, Y., & Boutros, J. (2012). On the ergodic rate for compute-and-forward. In 2012 International Symposium on Network Coding, NetCod 2012 (pp. 131-136). (2012 International Symposium on Network Coding, NetCod 2012). IEEE Computer Society.