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Fountain codes are a universal class of rateless codes originally designed for erasure channels. Naturally adapting to channel states without channel knowledge at the transmitter, fountain codes have recently been demonstrated also as an appealing solution for communication over fading channels. However, their relatively high decoding complexity limits their practical use in a wireless setting. In this paper, we present a simple modification of the decoding algorithm for Raptor codes - a type of fountain codes - over fading channels, where the complexity is significantly reduced without sacrifice of performance.