Coding theorems for reversible embedding

Abstract

We consider embedding of messages (data-hiding) into i.i.d. host sequences. As in Fridrich et al. [2002] we focus on the case where reconstruction of the host sequence from the composite sequence is required. We study the balance between embedding rate and embedding distortion. First we determine the distortion-rate region corresponding to this setup. Then we generalize this result in two directions. (A) The reversible embedding setup is not robust. Therefore we also consider reconstruction based on the output sequence of a discrete memoryless channel whose input is the composite sequence. We also determine the distortion-rate region for this setup. (B) Then we consider the case where only partial reconstruction of the host sequence is required. We determine the possible trade-offs here between embedding rate, distortion between source sequence and composite sequence (embedding distortion), and distortion between source sequence and restoration sequence (restoration distortion), i.e. the distortion-rate region. All achievability proofs in this paper are based on the Gelfand-Pinsker [1980] achievability proof.

Optimum reversible data hiding and permutation coding

“…The first relevant reversible data hiding algorithm was devised some years later by Fridrich et al [3], who proposed a method based on optimum compression of the least-significant bit plane of a host replacing its least-significant bit plane. However it was the work of Kalker and Willems which definitively set reversible watermarking on a sound footing, by revealing the information-theoretical limits of the problem (see [4], later generalised in [5] and [6]). This work showed that Fridrich et al's approach was only optimum for a particular distortion constraint.…”

Semantic coding: Partial transmission

“…In fact semantic compaction is identical to zero-rate reversible embedding [8], semantic transmission is the same as robust reversible embedding [9], and semantic compression is zerorate partially reversible embedding [10]. For an overview see [11]. Reversible embedding work has the same flavor as the work of Sutivong et al [12], [13], however there semantic distortion is absent.…”

Information Embedding in Degraded Broadcast Channels

“…In irreversible IE schemes, an estimate of only the message embedded in the host sequence is recovered at the decoder [2], [3], [4], [5]. In reversible IE schemes, both the embedded message and the host sequence are recovered at the decoder [6]. Given the various advantages and applications of IE, it is important to study fundamental performance limits of these schemes.…”