Complex field network coding for multiuser cooperative communications

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188 Scopus citations


Multi-source relay-based cooperative communications can achieve spatial diversity gains, enhance coverage and potentially increase capacity when multiuser detection is used to effect maximum likelihood demodulation. If considered for large networks, traditional relaying entails loss in spectral efficiency that can be mitigated through network coding at the physical layer. These considerations motivate the complex field network coding (CFNC) approach introduced in this paper. Different from network coding over the Galois field, where wireless throughput is limited as the number of sources increases, CFNC always achieves throughput as high as 1/2 symbol per source per channel use. In addition to improved throughput, CFNC-based relaying achieves full diversity gain regardless of the underlying signal-to-noise-ratio (SNR) and the constellation used. Furthermore, the CFNC approach is general enough to allow for transmissions from sources to a common destination as well as simultaneous information exchanges among sources.

Original languageEnglish (US)
Article number4481380
Pages (from-to)561-571
Number of pages11
JournalIEEE Journal on Selected Areas in Communications
Issue number3
StatePublished - Apr 2008

Bibliographical note

Funding Information:
Manuscript received May 29, 2007; revised October 26, 2007. This work was supported through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. This paper was presented in part at the 41st Conference on Information Sciences and Systems, Johns Hopkins University, NJ, Mar. 2007.


  • Complex field coding
  • Cooperative communications
  • Diversity gain
  • Linkadaptive regeneration
  • Multiuser detection
  • Network coding


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