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In this paper, we propose a computationally efficient algorithm for transmit power and bit allocations in wireless OFDM systems aiming at maximization of data rate under the constraint of total transmit power and bit error rate. Although the proposed algorithm is based on the water-filling approach, the computational complexity is only O(k×M), where k denotes the number of iterations required to meet the constraints and M is the number of subchannels. By computer simulations, we verify that 10 iterations are sufficient to satisfy the constraints, and the decrease of data rate for the proposed algorithm is shown to be less than one percent relative to the optimal method at the average SNR above 4 dB. The proposed algorithm is appropriate for OFDM systems in a time varying wireless channel for its low computational complexity and good performance.