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) ∈;ℝ^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.