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The MPEG-1 Layer III audio coding is most widespread digital audio format on the Internet. Its encoder is more complicated than the other layers in the MPEG-1 audio specification, where the bit allocation constitutes significant part of the total computational load. This paper describes a fast bit allocation technique using a novel linear model to compute the bitrate and the global gain of the inner loop (rate control loop) for the classic MP3 bit allocation problem. Estimated quantization noise is approximated with a binomial expansion for the adjustment of the scale-factors. This procedure reduces the outer loop iterations (distortion control loop) to one loop. Our bit allocation technique is about five times faster compared to the well-known LAME MP3 encoder. Based on the objective quality measure, total number of distorted bands, and average total noise-to-masking ratio (NMR), our experimental results show that there is significant improvement in speedup of the encoding process without noticeable audio quality degradation.