Permutation codes and steganography

We show that Slepian's Variant I permutation codes implement firstorder perfect steganography (i.e., histogram-preserving steganography). We give theoretical expressions for the embedding distortion, embedding rate and embedding efficiency of permutation codes in steganography, which demonstrate that these codes conform to prior analyses of the properties of capacity-achieving perfect stegosystems with a passive warden. We also propose a modification of adaptive arithmetic coding that near optimally implements permutation coding with a low complexity, confirming all our theoretical predictions. Finally we discuss how to control the embedding distortion. Permutation coding turns out to be akin to Sallee's model-based steganography, and to supersede both this method and LSB matching.