In this paper, A Parallel Combinatory-Orthogonal Frequency Division Multiplexing (PC-OFDM) system is proposed and analyzed. The proposed system selects at each symbol interval a subset of the available sub-carriers, and the selected sub-carriers are modulated by points from an M-PSK signal constellation. PC-OFDM systems can be designed to have lower Peak to Average Power Ratio (PAPR), higher bandwidth e ciency, and lower bit error probability on Gaussian channels compared to ordinary OFDM systems. A bit mapping procedure using the Johnson association together with a position algorithm for the PSK symbols is proposed. Good analytical approximations of the BER for PC-OFDM systems are derived for AWGN and Ricean fading channels, and extensive simulation results are presented.