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This correspondence investigates a noncoherent discrete-time memoryless Rayleigh-fading channel. A logarithmic transform converts it into an induced channel with additive noise that is independent of the channel input. From this perspective, it is natural and convenient for us to revisit several known results and gain new insights. In particular, we specify a class of simple, log-scale uniform channel input distributions that performs well for moderate to high signal-to-noise ratio (SNR). Furthermore, a continuous-amplitude log-scale uniform distribution is asymptotically capacity-achieving in the sense that the difference between the resulting mutual information and the channel capacity approaches zero as SNR becomes large. We also extend the induced additive-noise channel approach to memoryless multiple-antenna channels possibly with transmit, but without receive, spatial correlation.