Bounds and protocols for a rate-constrained relay channel

In this correspondence, a relay rate-constrained variation of the three-node relay channel is introduced and studied. In the rate-constrained relay channel, the relay cannot reliably decode or encode beyond a rate constraint ̄R. A cut-set upper bound, and rate-constrained variations of decode-and-forward and estimate-and-forward protocol are derived. It is observed that relative performance of the unconstrained protocols does not predict relative performance of the constrained protocols; that is, estimate-and-forward almost always offers superior performance for small rate constraints. A new metric, denoted as the relay efficiency, measures the slope at which the relay channel rate increases over the relay-less channel. While the cut-set upper bound has a relay efficiency of one for the Gaussian relay channel at ̄R = 0, the two new protocols do not. Finally, it is shown that an effective relay rate constraint can be computed for general relay protocols. To demonstrate this concept, a Markovian amplify-and-forward protocol, in which the relay does not perform any explicit encoding or decoding, is examined and compared to the introduced rate-constrained protocols.