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A new orthogonal frequency division multiplexing (OFDM) with reduced peak-to-average power ratio (PAPR) based on coded discrete cosine harmonic wavelet packet transform (DCHWPT), is proposed. In this method, tree pruning is done for the selection of a tree structure with minimum PAPR. To identify different tree structures, Gray code is used which is communicated as side information to the receiver. Also to improve bit error rate (BER) performance and reduce PAPR, Hadamard codes are employed. The proposed method based on DCHWPT exploits the desirable discrete cosine transform (DCT) properties like energy compaction/low leakage, better frequency resolution and its real nature, compared with those of discrete Fourier transform. Further, the harmonic wavelet employed has built in decimation without any associated antialiasing filters and easy reconstruction by concatenation of different scales in frequency (DCT) domain with no image rejection filters and complicated delay compensation makes the proposed wavelet packet simple in implementation. The proposed OFDM discrete cosine harmonic wavelet packet (DCHWP-OFDM) which leverages the advantages of DCHWPT has been used for BPSK modulated signals. The DCHWP-OFDM provides an improvement of PAPR reduction of 2.4 and 3.4 dB as compared with those of Haar and Daubechies-4 wavelet packet OFDM, respectively. This reduction in PAPR is with a BER performance in the range of 0.001-0.0001 at an signal-to-noise ratio of 10 dB.