High-resolution distributed functional quantization

In traditional modes of lossy compression, attaining low distortion letter-by-letter on a vector of source letters X₁ ^N=(X₁, X₂,..., X_N)isinRopf^N is the implicit aim. We consider here instead the goal of estimating at the destination a function G(X₁ ^N) of the source data under the constraint that each X_i must be separately scalar quantized. The design of optimal fixed- and variable-rate scalar quantizers is considered under the assumptions of high-resolution quantization theory, yielding optimal point densities for regular quantizers. Additionally, we consider how performance scales with N for certain classes of functions. This demonstrates potentially large improvement from consideration of G in the quantizer design.