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This paper analyzes the performance of Walsh-Hadamard coded modulation schemes that arise by traditional spreading and multiplexing of antipodal information bits with standard Walsh-Hadamard matrices, over fully interleaved flat Rayleigh fading channels. The resulting Pulse Amplitude Modulation (PAM) constellations are processed by an optimum Maximum A posteriori Probability (MAP) vector detector at the receiver, including external diversity combining. Tight upper and lower bounds are derived for the mean bit error probability, verified by extensive Monte Carlo simulations. The results show that the exploited inherent time diversity of the coded modulation scheme provides substantial gains over standard BPSK modulation for fully interleaved Rayleigh fading channels, without any bit rate reduction (for rate 1 codes) or mean symbol energy increase. The performance is enhanced by increasing the size of the Walsh-Hadamard matrices with the drawback of increased detection complexity and higher instant power variations.