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We present a new framework for rate-distortion (R-D) analysis, where the coding rate R and distortion D are considered as functions of ρ which is the percentage of zeros among the quantized transform coefficients. Previously (see He, Z. et al., Int. Conf. Acoustics, Speech and Sig. Proc., 2001), we observed that, in transform coding of images and videos, the rate function R(ρ) is approximately linear. Based on this linear rate model, a simple and unified rate control algorithm was proposed for all standard video coding systems, such as MPEG-2, H.263, and MPEG-4. We further develop a distortion model and an optimum bit allocation scheme in the ρ domain. This bit allocation scheme is applied to MPEG-4 video coding to allocate the available bits among different video objects. The bits target of each object is then achieved by our ρ-domain rate control algorithm. When coupled with a macroblock classification scheme, the above bit allocation and rate control scheme can also be applied to other video coding systems, such as H.263, at the macroblock level. Our extensive experimental results show that the proposed algorithm controls the encoder bit rate very accurately and improves the video quality significantly (by up to 1.5 dB).