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The reliability of usual Markov chain models for Rayleigh fading depends strongly on the channel variation regime. In this letter, a flat Rayleigh fading channel and RAKE receiver output model for all fading variation speeds is proposed. The complex Gaussian fading and the RAKE output processes are bandlimited. A variable-order Markov chain provides the desirable discrete process with suitable correlation properties at a frequency that respects the sampling theorem. An interpolator provides samples at the transmission rate. This model is available for all fading variation speeds, and the Markov chain is built only once. High soft-output reliability with important simulation time reduction is obtained.