Asymptotically Optimum Perfect Universal Steganography of Finite Memoryless Sources

TL;DR

This paper presents an asymptotically optimal universal steganography method for finite memoryless sources, extending it to include distortion constraints and demonstrating practical implementation via permutation coding and adaptive arithmetic coding.

Contribution

It introduces a new optimal steganography solution based on permutation coding, linking it to universal source coding, and addresses distortion constraints with a practical partitioned coding approach.

Findings

Permutation coding achieves asymptotically optimal embedding rate.

Adaptive arithmetic coding enables practical implementation.

Partitioned permutation coding effectively balances rate and distortion.

Abstract

A solution to the problem of asymptotically optimum perfect universal steganography of finite memoryless sources with a passive warden is provided, which is then extended to contemplate a distortion constraint. The solution rests on the fact that Slepian's Variant I permutation coding implements first-order perfect universal steganography of finite host signals with optimum embedding rate. The duality between perfect universal steganography with asymptotically optimum embedding rate and lossless universal source coding with asymptotically optimum compression rate is evinced in practice by showing that permutation coding can be implemented by means of adaptive arithmetic coding. Next, a distortion constraint between the host signal and the information-carrying signal is considered. Such a constraint is essential whenever real-world host signals with memory (e.g., images, audio, or video) are decorrelated to conform to the memoryless assumption. The constrained version of the problem requires trading off embedding rate and distortion. Partitioned permutation coding is shown to be a practical way to implement this trade-off, performing close to an unattainable upper bound on the rate-distortion function of the problem.