Consider a pair of correlated Gaussian sources (X1,X2). Two separate encodersobserve the two components and communicate compressed versions of theirobservations to a common decoder. The decoder is interested in reconstructing alinear combination of X1 and X2 to within a mean-square distortion of D. Weobtain an inner bound to the optimal rate-distortion region for this problem. Aportion of this inner bound is achieved by a scheme that reconstructs thelinear function directly rather than reconstructing the individual componentsX1 and X2 first. This results in a better rate region for certain parametervalues. Our coding scheme relies on lattice coding techniques in contrast tomore prevalent random coding arguments used to demonstrate achievable rateregions in information theory. We then consider the case of linearreconstruction of K sources and provide an inner bound to the optimalrate-distortion region. Some parts of the inner bound are achieved using thefollowing coding structure: lattice vector quantization followed by"correlated" lattice-structured binning.
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