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In this paper, a peak to average power ratio (PAPR) reduction scheme with low complexity and high performance for orthogonal frequency division multiplexing (OFDM) signals is proposed. The proposed scheme is a hybrid PAPR scheme that employs a two-stage cascade structure. The first stage is a post-IFFT stage that can construct a set of high-order quadrature amplitude modulation (QAM) sequences from QPSK or BPSK sequences with the smallest possible number of IFFTs. The second stage is based on an optimal Class-III selected mapping (SLM) scheme which consists of a bank of parallel blocks. Each of these blocks generates more candidate sequences from each of QAM sequences by passing it through a set of parallel sub-blocks that perform circular convolution with perfect sequences and circular shifting with optimum shift values. Simulation results show that the proposed scheme can outperform existing schemes in terms of PAPR reduction with lower complexity.