This paper proposes a novel Orthogonal frequency-division multiplexing (OFDM) system based on polynomial cancellation coded OFDM (PCC-OFDM). This proposed system can reduce peak-to-average power ratio (PAPR) by our neural phase rotator and it does not need any side information to transmit phase rotation factors. Moreover, this system can compensate the common phase error (CPE) by a proposed technique which allows estimating frequency offset at receiver. From numerical experiments, it is shown that our system can reduce PAPR and ICI at the same time and improve BER performance effectively.