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Fast Fourier Transform(FFT) represents a common communication pattern shared by a large class of scientific and engineering problems and wavelength assignment is a key issue to increase efficiency and reduce cost in Wavelength Division Multiplexing (WDM) optical networks. In this paper, we propose a new scheme for the wavelength assignment of parallel FFT communication pattern on WDM linear arrays. By lattice embedding, the number of wavelengths required to realize parallel FFT communication pattern on WDM linear arrays significantly improves the known result. Our proposed embedding method also provides a new approach to the hypercube layout problem considering connections dimension by dimension rather than all connections as in the traditional approach.