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A transmitter and receiver need to be designed to guarantee reliable communication on any channel belonging to a given family of finite-state channels defined over common finite input, output, and state alphabets. Both the transmitter and receiver are assumed to be ignorant of the channel over which transmission is carried out and also ignorant of its initial state. For this scenario we derive an expression for the highest achievable rate. As a special case we derive the compound channel capacity of a class of Gilbert-Elliott channels.