At present, mud pulse transmission systems are widely used in downhole data transmission. But the systems are very low in transmission efficiency, only 5-10 bits/s, with very large anti-inter-symbol-interference (ISI). It cannot meet high requirements for high-speed transmission of modern logging system. The development of communication technology has laid some foundation for this requirement. For this purpose, the Orthogonal Frequency Division Multiplexing (OFDM) Wireless Downhole Transmission Systems are proposed for the first time because of their high transmission rate, anti-inter-symbol-interference (ISI), and high spectral efficiency, etc. Due to non-linear power amplifier (PA) of logging systems with limited dynamic range, the drawbacks of high peak-average power ratio (PAPR) may outweigh all the potential benefits of OFDM wireless downhole transmission systems. Selective mapping (SLM) method can reduce the PAPR of OFDM logging signals without distortion. But at the receiver, the conventional SLM method needs exact bits of side information (SI) to recover the data signal. The probability of erroneous SI detection has a significant influence on the error performance of the system. And individual transmissions of SI result in the reduction of bandwidth efficiency. To restore the exact data signal, our scheme codes the SI bits by linear block codes (LBC), and is easily decoded by syndrome decoding. And then the coding SI bits are superimposed onto the logging signals to omit SI bits transmission. The theory and simulation results show that the proposed method has better performance than the conventional one. Accordingly, the OFDM wireless downhole transmission systems can tackle the high PAPR problem, and highten the transmission rate of logging signals.