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Variable length communication over a compound channel with feedback isconsidered. Traditionally, capacity of a compound channel without feedback isdefined as the maximum rate that is determined before the start ofcommunication such that communication is reliable. This traditional definitionis pessimistic. In the presence of feedback, an opportunistic definition isgiven. Capacity is defined as the maximum rate that is determined at the end ofcommunication such that communication is reliable. Thus, the transmission ratecan adapt to the channel chosen by nature. Under this definition, feedbackcommunication over a compound channel is conceptually similar to multi-terminalcommunication. Transmission rate is a vector rather than a scalar; channelcapacity is a region rather than a scalar; error exponent is a region ratherthan a scalar. In this paper, variable length communication over a compoundchannel with feedback is formulated, its opportunistic capacity region ischaracterized, and lower bounds for its error exponent region are provided..

Opportunistic capacity and error exponent regions for compound channel with feedback