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Orthogonal frequency-division multiplexing (OFDM) is the most popular modulation in modern wireless communication systems. Among other features, OFDM has been able to successfully exploit channel state information (CSI) at the transmitter, allowing to implement dynamic resource allocation schemes that improve spectral efficiency and error resilience. Nevertheless, in most wireless communication systems achieving a perfect CSI at the transmitter is difficult. For this reason a limited-rate feedback mode has been proposed, in which only quantized CSI at the transmitter is available. In this paper we design joint channel quantization and resource allocation schemes for single-user OFDM systems, that use limited-rate feedback and do not assume any structure on the channel quantizer. The new schemes are obtained by solving an optimization problem that maximizes average ergodic rate subject to average power and bit error rate constraints. Necessary optimality conditions for the quantization and resource allocation schemes are derived and algorithms to find a solution satisfying such conditions are discussed. Since finding the overall global optimal solution is computationally cumbersome, suboptimal yet simple schemes are also explored. Three simplifications are investigated, namely: a worst-case robust design that reduces the dimensionality of the problem; optimal and provably convergent stochastic schemes that catch the average behavior of the system on-the-fly; and schemes that reduce the amount of feedback required from the receiver by exploiting the channel correlation among subcarriers. The signalling and computational costs associated to the implementation of the developed schemes and their extension to multiple user systems are also discussed. Numerical examples corroborate analytical claims and reveal that significant gains result even when suboptimal schemes based on affordable limited-rate feedback are used.