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A new low peak-to-average power ratio (PAPR) transceiver is proposed for the coded single-carrier frequency division multiple access (SC-FDMA) system over frequency selective fading channels. By exploiting the constant envelope of the Chu-sequence in both frequency and time domains, the parallel spreading scheme and M-ary cyclic shift mapping technique can support the coded SC-FDMA system with a low PAPR for transmission at a high data rate. Interleaved time and frequency domain orthogonal modulation can increase the frequency diversity gain through the frequency domain equaliser and the time domain despreader. Moreover, the maximum likelihood rule is designed to detect the M-ary mapping data, which can provide M-ary gain to improve system performance. Simulation results reveal that the proposed high-rate coded SC-FDMA system can provide a lower PAPR and a better bit error rate (BER) performance than the conventional interleaved SC-FDMA system.