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Selected mapping (SLM) and partial transmit sequence (PTS) are well-known techniques for peak-power reduction in orthogonal frequency-division multiplexing (OFDM). We derive a simplified maximum likelihood (ML) decoder for SLM and PTS that operates without side information. This decoder exploits the fact that the modulation symbols belong to a given constellation and that the multiple signals generated by the PTS or SLM processes are widely different in a Hamming distance sense. Pairwise error probability (PEP) analysis suggests how SLM and PTS vectors should be chosen. The decoder performs well over additive white Gaussian noise (AWGN) channels, fading channels, and amplifier nonlinearities.