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Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding
- IEEE TRANS. ON INFORMATION THEORY
, 1999
"... We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing information-embedding rate, mini ..."
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Cited by 496 (14 self)
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We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing information-embedding rate, minimizing distortion between the host signal and composite signal, and maximizing the robustness of the embedding. We introduce new classes of embedding methods, termed quantization index modulation (QIM) and distortion-compensated QIM (DC-QIM), and develop convenient realizations in the form of what we refer to as dither modulation. Using deterministic models to evaluate digital watermarking methods, we show that QIM is "provably good" against arbitrary bounded and fully informed attacks, which arise in several copyright applications, and in particular, it achieves provably better rate distortion--robustness tradeoffs than currently popular spread-spectrum and low-bit(s) modulation methods. Furthermore, we show that for some important classes of probabilistic models, DC-QIM is optimal (capacity-achieving) and regular QIM is near-optimal. These include both additive white Gaussian noise (AWGN) channels, which may be good models for hybrid transmission applications such as digital audio broadcasting, and mean-square-error-constrained attack channels that model private-key watermarking applications.
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple point-to-point communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
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Cited by 345 (14 self)
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Network information theory promises high gains over simple point-to-point communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning scheme. Wyner and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, recent work proposed the idea of nested codes, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We review these recent developments and explore their tight relation to concepts such as combined shaping and precoding, coding for memories with defects, and digital watermarking. We also propose a few novel applications adhering to a unified approach.
Information-theoretic analysis of information hiding
- IEEE Transactions on Information Theory
, 2003
"... Abstract—An information-theoretic analysis of information hiding is presented in this paper, forming the theoretical basis for design of information-hiding systems. Information hiding is an emerging research area which encompasses applications such as copyright protection for digital media, watermar ..."
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Cited by 265 (19 self)
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Abstract—An information-theoretic analysis of information hiding is presented in this paper, forming the theoretical basis for design of information-hiding systems. Information hiding is an emerging research area which encompasses applications such as copyright protection for digital media, watermarking, fingerprinting, steganography, and data embedding. In these applications, information is hidden within a host data set and is to be reliably communicated to a receiver. The host data set is intentionally corrupted, but in a covert way, designed to be imperceptible to a casual analysis. Next, an attacker may seek to destroy this hidden information, and for this purpose, introduce additional distortion to the data set. Side information (in the form of cryptographic keys and/or information about the host signal) may be available to the information hider and to the decoder. We formalize these notions and evaluate the hiding capacity, which upper-bounds the rates of reliable transmission and quantifies the fundamental tradeoff between three quantities: the achievable information-hiding rates and the allowed distortion levels for the information hider and the attacker. The hiding capacity is the value of a game between the information hider and the attacker. The optimal attack strategy is the solution of a particular rate-distortion problem, and the optimal hiding strategy is the solution to a channel-coding problem. The hiding capacity is derived by extending the Gel’fand–Pinsker theory of communication with side information at the encoder. The extensions include the presence of distortion constraints, side information at the decoder, and unknown communication channel. Explicit formulas for capacity are given in several cases, including Bernoulli and Gaussian problems, as well as the important special case of small distortions. In some cases, including the last two above, the hiding capacity is the same whether or not the decoder knows the host data set. It is shown that many existing information-hiding systems in the literature operate far below capacity. Index Terms—Channel capacity, cryptography, fingerprinting, game theory, information hiding, network information theory,
Cognitive Radio: An Information-Theoretic Perspective
, 2009
"... We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has non-causal knowledge of the primary radio’s codeword. We characterize the largest rate at w ..."
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Cited by 183 (1 self)
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We consider a communication scenario in which the primary and the cognitive radios wish to communicate to different receivers, subject to mutual interference. In the model that we use, the cognitive radio has non-causal knowledge of the primary radio’s codeword. We characterize the largest rate at which the cognitive radio can reliably communicate under the constraint that (i) no rate degradation is created for the primary user, and (ii) the primary receiver uses a single-user decoder just as it would in the absence of the cognitive radio. The result holds in a “low interference ” regime in which the cognitive radio is closer to its receiver than to the primary receiver. In this regime, our results are subsumed by the results derived in a concurrent and independent work [24]. We also demonstrate that, in a “high interference ” regime, multi-user decoding at the primary receiver is optimal from the standpoint of maximal jointly achievable rates for the primary and cognitive users.
The duality between information embedding and source coding with side information and some applications
- in Proc. IEEE Int. Symp. Information Theory
, 2001
"... Abstract—Aspects of the duality between the information-embedding problem and the Wyner–Ziv problem of source coding with side information at the decoder are developed and used to establish a spectrum new results on these and related problems, with implications for a number of important applications ..."
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Cited by 87 (13 self)
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Abstract—Aspects of the duality between the information-embedding problem and the Wyner–Ziv problem of source coding with side information at the decoder are developed and used to establish a spectrum new results on these and related problems, with implications for a number of important applications. The singleletter characterization of the information-embedding problem is developed and related to the corresponding characterization of the Wyner–Ziv problem, both of which correspond to optimization of a common mutual information difference. Dual variables and dual Markov conditions are identified, along with the dual role of noise and distortion in the two problems. For a Gaussian context with quadratic distortion metric, a geometric interpretation of the duality is developed. From such insights, we develop a capacity-achieving information-embedding system based on nested lattices. We show the resulting encoder–decoder
Data-Hiding Codes
- Proc. IEEE
, 2005
"... This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital m ..."
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Cited by 58 (4 self)
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This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding, and covert communications. Some of these applications imply the presence of an adversary attempting to disrupt the transmission of information to the receiver; other applications involve a noisy, generally unknown, communication channel. Our focus is on the mathematical models, fundamental principles, and code design techniques that are applicable to data hiding. The approach draws from basic concepts in information theory, coding theory, game theory, and signal processing, and is illustrated with applications to the problem of hiding data in images. Keywords—Coding theory, data hiding, game theory, image processing, information theory, security, signal processing, watermarking. I.
Multiple user writing on dirty paper
- in Proc. IEEE ISIT’ 2004
, 1983
"... In “writing on dirty paper (WDP) ” [1], Costa considered a variation of the standard additive white Gaussian noise (AWGN) channel with the channel output given by Y n = Xn+Zn+Sn. Here the n-block input Xn has average power ..."
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Cited by 46 (0 self)
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In “writing on dirty paper (WDP) ” [1], Costa considered a variation of the standard additive white Gaussian noise (AWGN) channel with the channel output given by Y n = Xn+Zn+Sn. Here the n-block input Xn has average power
Multiaccess Channels with State Known to One Encoder: A Case of Degraded Message Sets
, 2007
"... We consider a state-dependent multiple access channel p(y|x1, x2, s) whose output Y is controlled by the channel inputs X1 and X2 from two encoders and the channel state S. It is assumed that the channel state is known non-causally at one encoder, called the informed encoder. We derive the capacity ..."
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Cited by 44 (5 self)
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We consider a state-dependent multiple access channel p(y|x1, x2, s) whose output Y is controlled by the channel inputs X1 and X2 from two encoders and the channel state S. It is assumed that the channel state is known non-causally at one encoder, called the informed encoder. We derive the capacity region for the case of degraded messages in which the informed encoder knows the message of the uninformed encoder.
The Gaussian MAC with conferencing encoders
- in IEEE Int. Symp. Information Theory
, 2008
"... Abstract—We derive the capacity region of the Gaussian version of Willems’s two-user MAC with conferencing encoders. This setting differs from the classical MAC in that, prior to each transmission block, the two transmitters can communicate with each other over noise-free bit-pipes of given capaciti ..."
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Cited by 40 (5 self)
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Abstract—We derive the capacity region of the Gaussian version of Willems’s two-user MAC with conferencing encoders. This setting differs from the classical MAC in that, prior to each transmission block, the two transmitters can communicate with each other over noise-free bit-pipes of given capacities. The derivation requires a new technique for proving the optimality of Gaussian input distributions in certain mutual information maximizations under a Markov constraint. We also consider a Costa-type extension of the Gaussian MAC with conferencing encoders. In this extension, the channel can be described as a two-user MAC with Gaussian noise and Gaussian interference where the interference is known non-causally to the encoders but not to the decoder. We show that as in Costa’s setting the interference sequence can be perfectly canceled, i.e., that the capacity region without interference can be achieved. I.
The Parallel-Gaussian Watermarking Game
- IEEE TRANS. ON INFORMATION THEORY
, 2000
"... Rates of reliable transmission of hidden information are derived for watermarking problems involving parallel Gaussian sources, which are often used to model host images and audio signals. Constraints are imposed on the average squared-error distortion that can be introduced by the information hider ..."
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Cited by 35 (5 self)
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Rates of reliable transmission of hidden information are derived for watermarking problems involving parallel Gaussian sources, which are often used to model host images and audio signals. Constraints are imposed on the average squared-error distortion that can be introduced by the information hider and by the attacker. When distortions are measured with respect to the original host data, the optimal covert and attack channels are two banks of Gaussian test channels. The solution to the watermarking game involves an optimal allocation of distortions by the information hider and by the attacker to the different channels. A fast algorithm is given for computing the optimal solution based on duality theory. For each channel we derive analytical expressions for two asymptotic regimes: weak and strong host signals. Finally we extend these results to the class of stationary Gaussian host signals with bounded, continuous spectral density. The analysis also provides an upper bound on watermarking capacity for non-Gaussian host signals.
