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This paper proposes a transmit power and bit allocation algorithm with constraint on allocated bit number. Transmit power and bit allocation algorithms help improve performance of OFDM systems, however the existing algorithms can't fully satisfy the need of baseband data modulation methods, which only map a certain number of input bits into a data symbol. The presented approach aims at maximization of data rate under constraint of number of input bits, as well as transmit power and bit error rate, and can be well adapted to practical OFDM systems in the condition of a fading channel. Simulation results show that the data rate for the proposed algorithm is close to the well known optimal greedy method which considers no constraint on the number of input bits, yet keep the computational complexity low.