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Orthogonal frequency division multiplexing (OFDM) systems for mobile applications suffer from inter-carrier-interference (ICI) due to frequency offset and to time-variation of the channels and from high peak-to-average-power ratio (PAPR). In this paper, we revisit symmetric cancellation coding (SCC) proposed by Sathananthan et al. and compare the effectiveness of SCC employing a fixed subtraction combining with the well-known polynomial cancellation coding (PCC) over Rayleigh fading channels with Doppler spread in terms of the signal-to-interference plus noise power ratio (SINR) and bit-error-rate (BER). We also compare our SCC employing subtraction combining with SCC of Sathananthan et al. employing maximum ratio combining (MRC). Our results show that, our SCC-OFDM gives higher SINR than PCC-OFDM over the flat Rayleigh fading channel, and that this superiority is not maintained under multi-path induced frequency-selective fading unless diversity combining is used. However, we show that, for frequency-selective fading channels, our SCC-OFDM in conjunction with differential modulation in frequency domain shows better performance than PCC-OFDM and normal OFDM for a certain range of Doppler spread. Finally, we also demonstrate that the SCC-OFDM signal has less PAPR compared to the normal OFDM and PCC-OFDM.