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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.

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