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In this letter the transmission power and interference threshold constraints for a cognitive OFDM system are converted to a normalized capacity of each OFDM subchannel. A simple but very efficient algorithm is proposed to allocate bits of all subchannels, which always picks the bit with the least cost. Simulation results show the proposed algorithm can obtain optimum solution in most cases. The remarkable characteristic of the algorithm is the computational complexity is very low and asymptotically constant for given radio scenarios, which meets the requirement of practical communication systems perfectly.