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The noncoherent symbol-by-symbol maximum a posteriori (MAP) detection and the soft-decision Viterbi decoding in a convolutionally coded frequency shift-keying (FSK) telemeter system are studied and the performance of coded FSK telemeter system in flat Rayleigh-fading channel is also analyzed. The coded bit metrics of FSK signal are calculated by MAP detector, and the bit metrics are applied in realization of soft-decision Viterbi decoding. The results show that the reliability of FSK telemeter system can be improved by MAP detection and soft-decision Viterbi decoding. Compared with the envelop detection and hard-decoding of coded FSK signal over flat Rayleigh-fading channel, the potential gain of 6-8 dB can be obtained by using MAP detection and soft-decision Viterbi detection.