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This dissertation is focused on the problem of rate allocation in a resource constrained environment and robustness of video coding over noise channels. A new rate allocation scheme that combines the traditional PCRD-Opt algorithm with the rho domain analysis is proposed for wavelet based image coders. The proposed scheme provides competitive performance as compared with the optimal PCRD-Opt algorithm, while with great reduction on complexity and computational costs. Rate allocation is developed for the Region-Of-Interest (ROI) in the wavelet transform domain for image coding. A recursive region growing method that deter mines the ROI in the transform domain is proposed. With excellent coding performance, robustness of the coder is improved as well because the ROI is allocated more bit resources and better protected. In addition, as intra-frame video coding is less vulnerable to errors than inter-frame video coding, we proposed rate allocation methods for several intra-frame video coding scenarios based on the proposed rate allocation algorithm for image coding. A coding method based on the principles of distributed source coding in the wavelet transform domain is proposed in order to achieve a good compromise between compression performance and robustness. 8x8 blocks in the wavelet transform domain are classified and coded by either distributed source coding or intra-frame video coding depending on the amount of correlation between co-located blocks in two consecutive frames. The regions that contain motion blocks are extracted and then intra coded with higher priority and more rate resources. The background regions are coded based on the principle of distributed video coding. The approach exploits inter-frame redundancy without explicitly using inter-frame video coding and demonstrated both a better robustness than the traditional intra-frame video coder H.263+ and improved compression performance over the image coder based intra-frame video coding.