Degraded Gaussian multirelay channel: Capacity and optimal power allocation

Alex Reznik, Sanjeev R. Kulkarni, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


We determine the capacity region of a degraded Gaussian relay channel with multiple relay stages. This is done by building an inductive argument based on the single-relay capacity theorem of Cover and El Gamal. For an arbitrary distribution of noise powers, we derive the optimal power distribution strategy among the transmitter and the relays and the best possible improvement in signal-to-noise ratio (SNR) that can be achieved from using a given number of relays. The time-division multiplexing operation of the relay channel in the wideband regime is analyzed and it is shown that time division does not achieve minimum energy per bit.

Original languageEnglish (US)
Pages (from-to)3037-3046
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2004

All Science Journal Classification (ASJC) codes

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


  • Capacity
  • Optimal resource allocation
  • Relay channel
  • Wideband channels


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