Robust Coding for Lossy Computing with Receiver-Side Observation Costs

TL;DR

This paper develops a robust coding framework for lossy computing where the decoder's measurements are noisy and controllable via actions, addressing uncertainties and extending classical source coding problems.

Contribution

It introduces a new rate-distortion-cost function for robust coding with noisy, controllable measurements, generalizing existing models like Heegard-Berger-Kaspi.

Findings

Derived the rate-distortion-cost function for the scenario.

Numerical examples illustrate optimal system design.

Extended classical source coding problems to include measurement noise and control.

Abstract

An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical problem, first studied by Yamamoto, is addressed here by including two new aspects: (i) The decoder obtains noisy measurements of its sequence, where the quality of such measurements can be controlled via a cost-constrained "action" sequence; (ii) Measurement at the decoder may fail in a way that is unpredictable to the encoder, thus requiring robust encoding. The considered scenario generalizes known settings such as the Heegard-Berger-Kaspi and the "source coding with a vending machine" problems. The rate-distortion-cost function is derived and numerical examples are also worked out to obtain further insight into the optimal system design.