Given a frequency-selective fading channel, feedback can be used to convey Channel State Information (CSI) and Receiver State Information (RSI) to the transmitter. RSI refers to information about the receiver’s estimate of the message, which can be used to improve reliability, e.g., through retransmissions. This paper studies the trade-off between these two types of feedback under total feedback constraint, assuming multi-carrier transmission through a doubly-selective Rayleigh fading channel. The objective is to maximize the error probability exponent. The CSI feedback scheme specifies particular groups of sub-channels over which uniform power is allocated, and the RSI feedback determines retransmissions of the codeword. The optimal tradeoff exhibits phase transitions which depends critically on the coherence time and the total amount of feedback. Specifically, the first few feedback bits should be allocated to CSI up to a critical amount. Additional feedback bits, if available, should first be allocated to RSI only, and then allocated to both CSI and RSI. This is because as the feedback rate increases beyond a certain amount, additional RSI feedback is not beneficial unless CSI feedback increases simultaneously.
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