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In this correspondence, we study the downlink throughput maximization for orthogonal frequency-division multiple-access (OFDMA) systems in the presence of feedback channel capacity constraints. We establish an information-theoretic lower bound on the capacity of feedback channel and build the corresponding test channel that achieves this lower bound. Based on the derived test channel, we formulate two optimization problems that maximize the downlink throughput with quantized channel state information (CSI): i) one problem where throughput is defined with the ergodic throughput and ii) the other problem with the outage throughput, from which we can see the performance limit for given limit feedback channels. We solve the throughput maximization problem through an iterative approach, which achieves the optimal ergodic throughput and the near-optimal outage throughput. Numerical results show that the downlink throughput with a limited feedback of CSI can be close to that with perfect CSI by exploiting correlation properties of downlink CSI for quantization.