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In this paper, permutation channels, which include the rank channels and doubly uniform channels, are defined. A lower bound on the capacities of these channels is obtained with help of nonparametric signal-detection theory. This bound reduces to the actual capacity for memoryless doubly uniform channels by properly selecting the associated nonparametric detectors, The lower bounds on the capacities of the rank channels are expressed in terms of Kendalrs rank correlation coefficient. When the signal power is low, the comparison between a rank channel and a memoryless binary symmetric channel is expressed in terms of the Pitman-Noether asymptotic relative efficiency.