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A discrete fading channel (DFC) consisting of a binary modulated time-correlated Rayleigh fading channel used in conjunction with coherent soft-decision demodulation of resolution q is considered. The capacity of the binary input 2q-ary output DFC, which can be explicitly expressed in terms of a non-binary noise discrete channel with stationary ergodic 2q-ary noise, is evaluated in terms of q and the fading parameters. It is observed that considerable capacity gains can be achieved due to the channel's statistical memory and the use of as few as 2 bits for soft-decision over interleaving the channel (to render it memoryless) and hard-decision demodulation (q = 1). The DFC is next fitted by a recently introduced analytically tractable queue-based (QB) Markovian noise model. The QB parameters are estimated via an iterative procedure that minimizes the Kullback-Leibler divergence rate between the DFC and QB noise sources. Modeling results, measured in terms of both channel noise correlation function and capacity reveal a good agreement between the two channels for a broad range of fading conditions.