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In this paper, we investigate a new digital communication system based on Walsh-Hadamard codes. The modulator maps a uniformly distributed binary source to a set of symbols with a Gaussian-like distribution. These symbols are then mapped to a 2-D constellation in such a way that performance is improved when transmission occurs over Rayleigh fading channels. We assess the performance of these modulation schemes when the channel is of the nonfrequency-selective Rayleigh fading plus white Gaussian noise type and compare the results to conventional quadrature-amplitude modulation (QAM) schemes with comparable spectral efficiencies. The proposed system provides excellent robustness to fading without the use of common diversity schemes employed in M-ary signaling systems to improve bit-error-rate (BER) performance in such environments.