Lossy Compression with Universal Distortion

TL;DR

This paper introduces a new lossy compression framework where the distortion measure is revealed only at run-time, analyzing its performance through rate redundancy and proposing multiple coding schemes.

Contribution

It presents a novel variant of $d$-semifaithful lossy coding with runtime distortion information and develops three different coding schemes with theoretical performance guarantees.

Findings

Achievability of rate redundancy bounds for the proposed schemes

Development of coding schemes using VC dimension, quantization, and random coding

Extension to cases where the distortion constraint is revealed at run-time

Abstract

We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at run-time. Two forms of rate redundancy are used to analyze the performance, and achievability results of both a pointwise and minimax nature are demonstrated. The first coding scheme uses ideas from VC dimension and growth functions, the second uses appropriate quantization of the space of distortion measures, and the third relies on a random coding argument.