## 1 Introduction  
Orthogonal frequency-division multiplexing (OFDM) is an effective technique for multicarrier systems due to its advantages of simplicity of equalization, high-rate data transmission and robustness against multipath fading. Currently, OFDM has been widely adopted by many modern wireless communication systems such as digital video broadcasting (DVB), digital audio broadcasting (DAB), wireless local area networks (WLAN) IEEE 802.11a, the WiMax standard IEEE 802.16 and long-term evolution (LTE). However, a high peak-to-average power ratio (PAPR) is one of the major problems associated with OFDM multicarrier systems, which may cause a severe degradation of bit error rate (BER) when it passes through a high-power amplifier (HPA) resulting in nonlinear distortion of the OFDM signal [1]. To deal with the high PAPR problem of the transmitted OFDM signals, many PAPR reduction techniques have been proposed [2; 3; 4; 5]. These techniques include clipping, coding, nonlinear companding transforms, constellation extension, partial transmit sequences (PTS) and selected mapping (SLM). Among these techniques, SLM is an effective PAPR reduction technique with high performance. However, the conventional SLM PAPR reduction scheme usually requires very high computational complexity. To reduce the computational complexity of the conventional SLM PAPR reduction scheme, many modified SLM PAPR reduction schemes have been proposed [6; 7; 8; 9; 10], most of which reduce the computational complexity of the conventional SLM PAPR reduction by decreasing the number of inverse fast Fourier transforms (IFFTs) involved in generating candidate signals. For instance, in [6], a modified SLM scheme was proposed to reduce the computational complexity of the conventional SLM PAPR reduction scheme, where the IFFT computations were reduced by generating a large number of the candidate signals from some of the remainder generated by IFFTs. In [7], [PERSON] and [PERSON] proposed the conversion matrices method to simplify the IFFT computations involved in the conventional SLM PAPR reduction scheme. Due to there only being two conversion matrices, the computational complexity of the conversion matrices method is only about half that of the conventional SLM PAPR reduction scheme. To further reduce the complexity, a large number of the conversion matrices were used to replace other IFFTs in [8]. With these conversion matrices, candidate signals were generated by only one or two IFFT outputs. The complexity in [8] is very low, but the BER performance is degraded due to the non-constant magnitudes of the frequency elements of the phase rotation vectors corresponding to the conversion matrices. In order to guarantee the BER performance of OFDM systems, new conversion matrices are designed in [9] based on the constant magnitudes of the frequency elements of the phase rotation vectors, but the proposed phase rotation vectors have a great correlation due to the periodic property, which leads to the performance loss of PAPR reduction. In [10], the candidate signals were generated by the linear combinations of the cyclically shifted interleaved partitions of the original OFDM signal. This method can achieve satisfactory PAPR reduction performance with greatly reduced computational complexity at the transmitter, but the receiver needs to detect and decode the transmitted side information (SI) with high computational complexity. However, all of the above SLM PAPR reduction schemes need the transmission of SI at the transmitter and perform the detection and decoding of SI at the receiver for correct data demodulation. In practice, the transmission of SI must be protected at the transmitter by using the channel coding method due to the frequency selective fading channel, and it is very important to correctly detect and decode the SI at the receiver since an erroneous detection of the SI will corrupt the entire received OFDM signal. This will further reduce the system throughput and increase the computational complexity at both the transmitter and receiver.