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In this paper, we analyze the performance of soft decision decoded, synchronous, fast frequency-hopping spread-spectrum multiple-access networks using M-ary frequency shift keying in Rayleigh fading channels under the assumption that the number of frequency hopping slots is sufficiently large. The joint probability density function (pdf) of the absolute values of the correlator outputs is derived to compute the channel capacity and evaluate the soft decision decoding performance of the 3GPP Turbo and convolutional codes. Results indicate that soft decision decoding based on the derived pdf drastically outperforms traditional decoders based on the Gaussian approximation of the effect of the multiple access interference (MAI). The sensitivity of the derived soft decision decoder to estimation errors in system parameters and the required computational complexities of the derived soft decision decoding metrics are also investigated.