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We study the capacity of a noncoherent time-selective block fading channel, under the assumption that the channel changes slowly over the block period N rather than remaining constant. The predictability of the channel is characterized through the rank Q (1 ≤ Q ≤ N) of the correlation matrix of the vector of channel gains over the block. The model includes the standard block fading model and the i.i.d. fading model as special cases. For large SNR, we prove that the capacity grows logarithmically with SNR with a slope of N-Q/N (for 1 ≤ Q ≤ N). For fixed SNR and Q, we show that the capacity approaches the coherent channel capacity when N→∞. We also characterize the asymptotics of the capacity in the regime where both N and Q→∞, with Q/N being kept constant. The results of the paper can be generalized to include multiple antennas and frequency-selectivity.