Distributed Functional Scalar Quantization Simplified

TL;DR

This paper simplifies the decoder design in distributed functional scalar quantization, extends its applicability to sources with infinite support, and validates the approach through simulations showing accurate performance predictions.

Contribution

It introduces a simpler decoder with equivalent asymptotic performance, decouples communication and computation, and extends DFSQ to infinite-support distributions.

Findings

Simpler decoder matches previous performance asymptotically.

Decoupled communication and computation blocks.

Performance predictions align with simulation results at moderate rates.

Abstract

Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works: prohibitively expensive decoder design and a restriction to sources with bounded distributions. We rigorously show that a much simpler decoder has equivalent asymptotic performance as the conditional expectation estimator previously explored, thus reducing decoder design complexity. The simpler decoder has the feature of decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to acquire sources with infinite-support distributions such as Gaussian or exponential distributions. Finally, through simulation results we demonstrate that performance at moderate coding rates is well predicted by the asymptotic analysis, and we give new insight on the rate of convergence.