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This paper presents an improved orthogonal frequency division multiplexing (OFDM) for asymmetric digital subcarrier loop (ADSL) system with discrete multi-tone (DMT) modulation and wireless communication. The proposed approach is based on discrete cosine transform (DCT) and utilize discrete Walsh-Hadamard transform (WHT) as a precoder. The bit-error rate (BER) performance of the proposed scheme is mathematically evaluated and by simulation over multipath fading channel and zero-padding minimum mean-square-error (ZP-MMSE) detection. Analytical results corroborated by computer simulation show that when real modulation format is used, the proposed scheme provides valuable signal-to-noise ratio (SNR) gain compared to the DCT-DMT and DFT-DMT. Additionally, the proposed scheme is found to be feasible for wireless communication where it achieves a significant SNR gain. Moreover, in comparison to DFT-DMT and DCT-DMT systems, the proposed scheme achieves reasonable reduction in peak-to-average power ratio (PAPR). Complexity analysis of the proposed compound transform is also presented in this work.