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This paper addresses the problem of optimal rate allocation for multiple description coding with redundant signal expansions. In case of redundant descriptions, the quantization of the transform coefficients has clearly to be adapted to the importance of the basis functions, to the redundancy in the representation, and to the expected loss probability on the transmission channel. We derive a rate-distortion optimal solution for the scalar quantization of coefficients in redundant signal representations. The application of the optimal rate allocation to a typical image communication problem demonstrates performance gains with respect to scheme based on uniform quantization with fixed step size, and to solutions based on unequal error protection.