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An optimal subband bit allocation technique for optimal distribution of bits among the subbands is presented. The proposed technique is based on a new rate-distortion model, which switches between two types of models at lower and higher bit rates. Based on this model, it is possible to select the best R-D strategy among the lower bit rate model, the higher bit rate model and the average between them. The Lagrangian optimisation method is then used to minimise this distortion model for a given bit budget and to obtain an optimum bit distribution among the subbands. The proposed optimal bit allocation framework is implemented on the motion-compensated 2D subband/DCT scalable video codec, which provides quality signal-to-noise ratio (SNR) scalability. The results show that the proposed bit allocation method outperforms the uniform allocation of bits over a wide range of target bit rates. Moreover, simulation results show that the performance of the presented scalable video coding is slightly inferior to the single layer H.264/AVC but outperforms the SNR scalability supported in joint scalable video model (JSVM), the state-of-the-art scalable video coding standard, that achieves its gain through the hierarchical B-pictures.