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This paper compares the partial-decode-forward and the complete-decode-forward coding strategies for the half-duplex Gaussian single-relay channel. The authors analytically show that the rate achievable by partial-decode-forward outperforms that of the more straightforward complete-decode-forward by at most 12.5%. Furthermore, in the following asymptotic cases, the gap between the partial-decode-forward and the complete-decode-forward rates diminishes: when the relay is close to the source, when the relay is close to the destination, and when the SNR is low. In addition, when the SNR increases, this gap, when normalized to the complete-decode-forward rate, also diminishes.
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