Multiple descriptions have been widely investigated as a quality of service technology for the delivery of multimedia information over lossy channels. This paper presents generalized methods for transform based multiple descriptions that do not introduce additional distortion to the transformed information. Previous noiseless methods place restrictions on how the information may be quantized prior to correlation. Typically, the information must be quantized with quasi-uniform quantizers which all have the same quantization step size. This paper expands these methods so that the information may be quantized with any quantizer, and different parts of the information may be quantized with different quantization step sizes. For specific correlating transforms, we propose a computationally efficient correlation transform that makes use of the Hadamard matrix
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