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This paper proposes a wireless system with a blind receiver which jointly performs noncoherent channel estimation and serially-concatenated turbo code decoding over fast time-varying Rayleigh-fading channels. The low complexity blind receiver consists of two parts: 1) a Kalman filter as its channel estimation part and 2) two decoders, including a differential decoder and a convolutional decoder, as its signal decoding part. With various soft information, calculated in the maximum likelihood sense, iteratively passed around between the channel estimator and the signal decoder, the system is expected to hopefully approach the optimal performance. Note that, with no training data in the proposed system, it is impossible for the Kalman filter to avoid the CSI (channel state information) phase ambiguity problem, which can be perfectly taken care of by the differential decoder. Computer simulations confirm that the proposed system exhibits robustness against fast time-variation of Rayleigh-fading channels.