The Rate-Distortion-Deception Tradeoff

2026-07-28

AI Summary

This study addresses the problem of compressing random variables under three simultaneous constraints: distortion (fidelity), perceptual naturalness, and a newly introduced deception constraint that requires reconstructed samples to appear as if drawn from a target distribution. By incorporating this deception constraint into the classical rate–distortion framework, the work extends traditional information-theoretic analysis to cross-distribution camouflage scenarios. Leveraging an information-theoretic formulation combined with distributional distance measures, the authors derive fundamental limits of compression under deception and establish a precise trade-off among rate, distortion, and deception. This theoretical advance provides a new foundation for applications such as privacy-preserving data release and adversarial data obfuscation.

Abstract

The problem of finding the optimal compression rate for a given random variable has been traditionally studied under two main constraints: distortion and perception. The distortion constraint enforces the fidelity of our reconstruction with respect to the observed realization of the random variable, while the perception constraint ensures that the reconstruction is close to a sample from the distribution of the random variable of interest. In this work, we explore the possibility of reconstruction, such that the reconstructed sample is still within a desired fidelity level with our original realization of the random variable, but at the same time, it resembles a sample from a different target distribution. We term this criterion as the deception constraint and find the fundamental tradeoffs of rate-distortion and deception.

Problem

• rate-distortion
• perception
• deception
• compression
• reconstruction

Innovation

• Rate-Distortion
• Deception Constraint
• Perception
• Distribution Mismatch
• Information Bottleneck