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Multimedia applications such as video streaming and mobile TV are emerging as the most promising applications over wireless networks. The increased coding efficiency and network friendly architecture of the latest video coding standard H.264/AVC has facilitated the delivery of coded video content to wireless users. However, wireless networks allow lower transmission bit-rates than wired networks while the display resolution of mobile devices is generally smaller than that of standard definition (SD) TV. This calls for fast bit-rate reduction techniques through video transcoding that can deliver the best video quality to the mobile receiver while adhering to the bit-rate constraints of the wireless network. In this paper, we present a bit-rate estimation model that speeds up the transcoding process by predicting the transcoded video bit-rate for different spatial resolution reduction ratios and quantization steps. We demonstrate that, on average, our proposed model can accurately estimate the bit-rate of the transcoded video to within 5% of the actual bit-rate of the transcoded video.