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The authors 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, they 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.
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