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The objective of joint source channel coding (JSCC) is to optimally allocate the available channel bandwidth between source coding and channel coding in order to minimize the average distortion in the presence of packet losses. Unlike previous research, which focuses on determining distortion-optimized methods for JSCC using either assumptions about the rate-distortion (R-D) curve properties of source data (e.g., convexity) or experimental R-D data, we explicitly employ the analytical operational R-D model of a three-dimensional wavelet video coder to solve the JSCC problem. Using this model, we formulated the JSCC optimization as a nonlinear programming (NP) problem. By expressing the NP problem in terms of a dynamic programming equation, we derived the necessary conditions that facilitate the search for global optimal solutions. In this letter, we focus on finding the optimal JSCC problem for subband video coding and not on deriving computationally efficient methods for JSCC.