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Opportunistic capacity and error exponent regions for variable length communication over compound channel with feedback

Variable length communication over a compound channel with feedback is considered. Traditionally, capacity of a compound channel is defined as the maximum rate at which reliable communication can be guaranteed before the start of communication. This is a pessimistic point of view. In this paper, we give an opportunistic definition of capacity. We define capacity as the maximum rate at which reliable communication can be guaranteed for the current choice of the channel by nature. Under this definition, a compound channel is conceptually similar to multi-terminal communication. Transmission rate is a vector rather than a scalar; channel capacity is a region rather than a scalar; error exponent is a region rather than a scalar. We formulate variable length communication over a compound channel with feedback, characterize its opportunistic capacity region, and provide lower bounds for the error exponent region.