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We consider a multiterminal source coding problem in which a source isestimated at a central processing unit from lossy-compressed remoteobservations. Each lossy-encoded observation is produced by a remote sensorwhich obtains a noisy version of the source and compresses this observationminimizing a local distortion measure which depends only on the marginaldistribution of its observation. The central node, on the other hand, hasknowledge of the joint distribution of the source and all the observations andproduces the source estimate which minimizes a different distortion measurebetween the source and its reconstruction. In this correspondence, weinvestigate the problem of optimally choosing the rate of each lossy-compressedremote estimate so as to minimize the distortion at the central processing unitsubject to a bound on the overall communication rate between the remote sensorsand the central unit. We focus, in particular, on two models of practicalrelevance: the case of a Gaussian source observed in additive Gaussian noiseand reconstructed under quadratic distortion, and the case of a binary sourceobserved in bit-flipping noise and reconstructed under Hamming distortion. Inboth scenarios we show that there exist regimes under which having more remoteencoders does reduce the source distortion: in other words, having fewer,high-quality remote estimates provides a smaller distortion than having more,lower-quality estimates.

Optimal Rate Allocation in Mismatched Multiterminal Source Coding