Bounds on the capacity of the relay channel with noncausal state at the source

Abdellatif Zaidi, Shlomo Shitz Shamai, Pablo Piantanida, Luc Vandendorpe

Research output: Contribution to journalArticlepeer-review


We consider a three-terminal state-dependent relay channel with the channel state available noncausally at only the source. Such a model may be of interest for node cooperation in the framework of cognition, i.e., collaborative signal transmission involving cognitive and noncognitive radios. We study the capacity of this communication model. One principal problem is caused by the relay's not knowing the channel state. For the discrete memoryless (DM) model, we establish two lower bounds and an upper bound on channel capacity. The first lower bound is obtained by a coding scheme in which the source describes the state of the channel to the relay and destination, which then exploit the gained description for a better communication of the source's information message. The coding scheme for the second lower bound remedies the relay's not knowing the states of the channel by first computing, at the source, the appropriate input that the relay would send had the relay known the states of the channel, and then transmitting this appropriate input to the relay. The relay simply guesses the sent input and sends it in the next block. The upper bound accounts for not knowing the state at the relay and destination. For the general Gaussian model, we derive lower bounds on the channel capacity by exploiting ideas in the spirit of those we use for the DM model; and we show that these bounds are optimal for small and large noise at the relay irrespective to the strength of the interference. Furthermore, we also consider a relay model with orthogonal channels from the source to the relay and from the source and relay to the destination in which the source input component that is heard by the relay does not depend on the channel states. We establish a better upper bound for both DM and Gaussian cases and we also characterize the capacity in a number of special cases.

Original languageEnglish
Article number6361299
Pages (from-to)2639-2672
Number of pages34
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 2013


  • Channel state information (CSI)
  • cognitive radio
  • dirty paper coding (DPC)
  • relay channel (RC)
  • user cooperation

All Science Journal Classification (ASJC) codes

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


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