Analysis of the Generalized DF-CF for Gaussian Relay Channels: Decode or Compress?

We consider a three-node quasi-static communication system with a full-duplex relay. The goal is to determine the relaying mode that enables rate-efficient communication under given channel conditions. To achieve this goal, we consider a generalized scheme that subsumes the decode-and-forward (DF) and compress-and-forward (CF) schemes as special cases. The generalized scheme is considered when the source and relay signals are synthesized from commonly-used Gaussian codebooks, which are shown to be capacity achieving in two asymptotic cases: perfect relay-destination link and broken source-destination link. Studying the generalized DF-CF scheme, it is shown that, for two non-asymptotic cases in which the signal-to-noise ratios (SNRs) of the links satisfy certain conditions, this scheme reduces to either DF or CF. For another set of non-asymptotic SNRs, the generalized scheme is shown to yield strictly higher rates than both DF and CF. Despite the complexity of the generalized scheme, its rate advantage over DF and CF is shown to be upper bounded by 0.5 bits per channel use. This indicates that the practical benefit of the analysis of this scheme is to enable selecting the relaying mode that suits a given channel realization. Numerical results show that, under Rayleigh fading conditions, this selection yields significant gains over fixed DF and CF.