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In this paper, we study a quantized feedback scheme to maximize the goodput of a finite blocklength communication scenario over a quasi-static fading channel. It is assumed that the receiver has perfect channel state information (CSI) and sends back the CSI to the transmitter over a resolution-limited error-free feedback channel. With this partial CSI, the transmitter is supposed to select the optimum transmission rate, such that it maximizes the overall goodput of the communication system. This problem has been studied for the asymptotic blocklength regime, however, no solution has so far been presented for finite blocklength. Here, we study this problem in two cases: with and without constraint on reliability. We first formulate the optimization problems and analytically solve them. Iterative algorithms that successfully exploit the system parameters for both cases are presented. It is shown that although the achievable maximum goodput decreases with shorter blocklengths and higher reliability requirements, significant improvement can be achieved even with coarsely quantized feedback schemes.

Goodput Maximization With Quantized Feedback in the Finite Blocklength Regime for Quasi-Static Channels