Optimal Distributed Codes for Feedback-Aided Cooperative Relay Networks

Francis Lu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A novel transmission scheme for cooperative relay networks is presented in this paper. The proposed scheme is based on the non-orthogonal selection decode-and-forward protocol with an additional assumption of having a low rate feedback channel from the destination to relays. Benefited from the feedback information, an optimal distributed code that has an extremely short delay equal to four is constructed, and the same code is applicable to networks with the arbitrary number of relays to yield optimal cooperative diversity. The proposed code is sphere decodable with a decoding complexity again independent of the number of relays in high SNR regime. In particular, when operating at multiplexing gain ≥(1/2), the lattice decoder at the destination has a zero complexity exponent, meaning a constant decoding complexity and independent of transmission rate. Analyses for the decoding complexity of other existing diversity-optimal distributed codes are also provided. It is shown that these codes have a linear growth in delay and an exponential growth in decoding complexity as the number of relays increases.

Original languageEnglish
Article number7469813
Pages (from-to)4198-4211
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - 1 Jul 2016


  • complexity exponents
  • Cooperative relay networks
  • cyclic division algebra
  • distributed codes
  • diversitymultiplexing gain tradeoff
  • feedback channel
  • Sphere decoder


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