On the error exponent for memoryless flat fading channels with channel-state-information feedback

We derive the random coding error exponent for the time-independent flat fading channel with perfect knowledge of the channel state information (CSI) at both the receiver and the transmitter. That is, the CSI is feedback from the receiver to the transmitter. In such a situation, the transmitter is capable of optimizing the power allocation of the transmitted signal according to the fading state in order to obtain, for our case, the best error exponent. The power scheme obtained here is different from the water-pouring one, which is known to maximize the channel capacity.