Robust Coding for Lossy Computing with Observation Costs

TL;DR

This paper studies a robust lossy coding problem where an encoder and decoder collaborate under measurement noise, costs, and failures to efficiently compute a function of their sequences, generalizing several classical problems.

Contribution

It introduces a new framework incorporating measurement costs and failures into lossy coding for function computation, extending classical models.

Findings

Derived the rate-distortion-cost function for special cases.

Provided upper and lower bounds for the general scenario.

Numerical examples illustrate optimal system design insights.

Abstract

An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise 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, which is taken at the decoder or at the encoder; (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 in relevant special cases, along with general upper and lower bounds. Numerical examples are also worked out to obtain further insight into the optimal system design.