## Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding (1999)

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Venue: | IEEE TRANS. ON INFORMATION THEORY |

Citations: | 355 - 12 self |

### BibTeX

@ARTICLE{Chen99quantizationindex,

author = {Brian Chen and Gregory W. Wornell},

title = {Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding},

journal = {IEEE TRANS. ON INFORMATION THEORY},

year = {1999},

volume = {47},

number = {4},

pages = {1423--1443}

}

### Years of Citing Articles

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### Abstract

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.

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Citation Context ...distortion constraint and a memoryless channel with known pdf where and are the th components of and , respectively. 13 Then, the super-channel is also memoryless and has probability law The capacity =-=[31] o-=-f this super-channel is the reliable information-embedding rate that is asymptotically achievable with long signal lengths . In nonwatermarking contexts, Gel’fand and Pinsker [32] and Heegard and El... |

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Citation Context ...form where is typically a pseudo-noise sequence. Such embedding methods are often referred to as additive spread-spectrum methods, and some of the earliest examples are described in [24], [25], [10], =-=[26]-=-, [11], [12]. Typically, takes the form where is a unit-energy spreading vector and is a scalar function of the message. 3 It is often convenient to view additive spread-spectrum as perturbation of a ... |

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Citation Context ...ortion-constrained, Gaussian information embedding is equivalent to power-constrained communication over a Gaussian channel with Gaussian side information known at the encoder, a case for which Costa =-=[34]-=- has determined the capacity to be, expressed in terms of the (embedding induced) DNR DNR DNR (38) 16 Indeed, these models can even apply to optimal, i.e., rate-distortion achieving [31], lossy compre... |

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Citation Context ...early combining the host signal with a small pseudo-noise signal that is modulated by the embedded signal, have received considerable attention in the literature as an alternative to LBM-type methods =-=[10]��-=-�[13]. In this paper, we show that both LBM-type strategies and additive spread spectrum are, in general, not good choices for most information embedding and digital watermarking applications. As an a... |

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Citation Context ...terms of the set of desired tolerable perturbation vectors for every given input. III. CLASSES OF EMBEDDING METHODS An extremely large number of embedding methods have been proposed in the literature =-=[22]-=-, [23], [1]. Broadly, for our purposes these can be divided into two classes: 1) host-interference nonrejecting methods and 2) host-interference rejecting methods. 2 Cox et al. have also recognized th... |

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Citation Context ...s of QIM in both cases. A. Attacks on Private-Key Systems Although the attacker does not know the key in a private-key scenario, he or she may know the basic algorithm used to embed the watermark. In =-=[16], Mo-=-ulin and O’Sullivan model such a scenario by assuming that the attacker knows the codebook distribution, but not the actual codebook. As we now develop, exploiting results of Moulin and O’Sullivan... |

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Citation Context ...into the design, performance evaluation, and implementation of QIM embedding methods, particularly those of low complexity. A convenient structure to consider is that of so-called dithered quantizers =-=[29]-=-, [30], which have the property that the quantization cells and reconstruction points of any given quantizer in the ensemble are shifted versions of the quantization cells and reconstruction points of... |

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Citation Context ...1 + DNR. Since the capacity in bits per dimension (bits per host signal sample) is given by (38), and there are two independent host signal samples per second for every Hertz of host signal bandwidth =-=[28], th-=-e capacity in bits per second per Hertz is C = log 2(1 + DNR) b/s/Hz. (42) Taking the ratio between (42) and (41), we see that the “value” in embedded rate of each dB drop in received host signal ... |

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Citation Context ...s of the set of desired tolerable perturbation vectors P{n|s} for every given input. 3 Classes of Embedding Methods An extremely large number of embedding methods have been proposed in the literature =-=[22, 23, 1]-=-. Broadly, for our purposes these can be divided into two classes: (1) host-interference non-rejecting methods and (2) host-interference rejecting methods. Host-interference non-rejecting methods have... |

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Citation Context ... dither modulation, digital watermarking, hybrid transmission, information embedding, quantization index modulation (QIM), steganography. I. INTRODUCTION ANUMBER of applications have emerged recently =-=[1] that requir-=-e the design of systems for embedding one signal, sometimes called an “embedded signal” or “watermark,” within another signal, called a “host signal.” The embedding must be done such that ... |

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Citation Context ... functions of the form where is typically a pseudo-noise sequence. Such embedding methods are often referred to as additive spread-spectrum methods, and some of the earliest examples are described in =-=[24]-=-, [25], [10], [26], [11], [12]. Typically, takes the form where is a unit-energy spreading vector and is a scalar function of the message. 3 It is often convenient to view additive spread-spectrum as ... |

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Citation Context ...here is typically a pseudo-noise sequence. Such embedding methods are often referred to as additive spread-spectrum methods, and some of the earliest examples are described in [24], [25], [10], [26], =-=[11]-=-, [12]. Typically, takes the form where is a unit-energy spreading vector and is a scalar function of the message. 3 It is often convenient to view additive spread-spectrum as perturbation of a projec... |

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Citation Context ...rference nonrejecting methods and 2) host-interference rejecting methods. 2 Cox et al. have also recognized that one may view watermarking as communications with side information known at the encoder =-=[21]-=-. Fig. 2. Equivalent super-channel model for information embedding. The composite signal is the sum of the host signal, which is the state of the super-channel, and a host-dependent distortion signal.... |

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Citation Context ...s super-channel is the reliable information-embedding rate that is asymptotically achievable with long signal lengths . In nonwatermarking contexts, Gel’fand and Pinsker [32] and Heegard and El Gama=-=l [33]-=- have determined the capacity of such a channel in the case of a random state vector with independent and identically distributed (i.i.d.) components when the encoder sees the entire state vector befo... |

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Citation Context .... In the case of watermarking, the maximization (32) is subject to a distortion constraint . A formal proof of the extension of (32) to include this constraint is developed in [20]. Other researchers =-=[18]-=-, [19], [16] are working on extending or have extended these results to the case where the channel law is not fixed but rather is chosen by an attacker subject to a distortion constraint. A related in... |

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Citation Context ...s typically a pseudo-noise sequence. Such embedding methods are often referred to as additive spread-spectrum methods, and some of the earliest examples are described in [24], [25], [10], [26], [11], =-=[12]-=-. Typically, takes the form where is a unit-energy spreading vector and is a scalar function of the message. 3 It is often convenient to view additive spread-spectrum as perturbation of a projection. ... |

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(Show Context)
Citation Context ...of the set of desired tolerable perturbation vectors for every given input. III. CLASSES OF EMBEDDING METHODS An extremely large number of embedding methods have been proposed in the literature [22], =-=[23]-=-, [1]. Broadly, for our purposes these can be divided into two classes: 1) host-interference nonrejecting methods and 2) host-interference rejecting methods. 2 Cox et al. have also recognized that one... |

74 | Some general methods for tampering with watermarks
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Citation Context ...copying by some duplication device that checks the embedded signal before proceeding with duplication. Such a system has been proposed for allowing a copy-once feature in digital video disc recorders =-=[2]-=-. Alternatively, a standards-compliant player could check the watermark before deciding whether or not to play the disc [3]. Other applications include automated monitoring of airplay of advertisement... |

72 | On lattice quantization noise
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Citation Context ...he design, performance evaluation, and implementation of QIM embedding methods, particularly those of low complexity. A convenient structure to consider is that of so-called dithered quantizers [29], =-=[30]-=-, which have the property that the quantization cells and reconstruction points of any given quantizer in the ensemble are shifted versions of the quantization cells and reconstruction points of any o... |

68 | The duality between information embedding and source coding with side information and some applications
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Citation Context ... and the asymptotic performance limits of coded QIM using information-theoretic analysis. Other emerging information-theoretic results on the digital watermarking problem are developed in, e.g., [14]�=-=��[20]-=-. The specific organization of the paper is as follows. In Section II, we develop two useful equivalent models for the information-embedding problem. In Section III, we classify traditional approaches... |

63 |
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Citation Context ...ethod is, the higher the robustness that can be achieved. A great many information-embedding algorithms have been proposed [1] in this still emerging field. Some of the earliest proposed methods [8], =-=[9]-=-, [7] employ a quantize-and-replace strategy: after first quantizing the host signal, these systems change the quantization value to embed information. A simple example of such a system is the so-call... |

46 | Performance analysis of a 2-D multipulse amplitude modulation scheme for data hiding and watermarking still images
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(Show Context)
Citation Context ... combining the host signal with a small pseudo-noise signal that is modulated by the embedded signal, have received considerable attention in the literature as an alternative to LBM-type methods [10]�=-=��[13]-=-. In this paper, we show that both LBM-type strategies and additive spread spectrum are, in general, not good choices for most information embedding and digital watermarking applications. As an altern... |

37 |
Nearest neighbor decoding for additive non-gaussian noise channels
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Citation Context ...ity as we show below. We consider the case of dither signals with 20 This rate is also the capacity when � is non-Gaussian, but still independent of �, and a correlation detector is used for decod=-=ing [35]-=-. a uniform distribution over the interval . In this case where the quantization error is uniformly distributed over the interval and statistically independent of [29]. Thus, the achievable rate is sl... |

35 |
Design and analysis of digital watermarking, information embedding, and data hiding systems
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Citation Context ...uction point, then (14) can be rewritten as (15) (While the minimum-distance decoder is especially convenient to implement and analyze, a variety of other potentially useful decoders are discussed in =-=[27]-=-.) Intuitively, the minimum distance measures the size of perturbation vectors that can be tolerated by the system. For example, if channel perturbations are bounded according to 7 (16) then the minim... |

26 | Quantization Index Modulation Methods for Digital Watermarking and Information Embedding of Multimedia
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(Show Context)
Citation Context ... same for each length- block. iii) The th block of is quantized with the dithered quantizer using the dither sequence . A detailed assessment of the complexity of this QIM realization is developed in =-=[15]-=-, [27]. The minimum-distance properties of coded binary dither modulation are readily deduced. In particular, any two distinct coded bit sequences differ in at least places, where is the minimum Hammi... |

25 |
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Citation Context ...emental information such as station identification or traffic information. More generally, the host signal in these hybrid transmission systems could be some other type of analog signal such as video =-=[7], -=-or even a digital waveform—for example, a digital pager signal could be embedded within a digital cellular telephone signal. In general, designers of information embedding systems for these kinds of... |

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Citation Context ...ily on the “host-blind” case of interest in most applications, where is not available to the decoder, in contrast to the “known-host” case, where the decoder can separately observe . (See, e.g=-=., [14] [17]-=- for information-theoretic treatments of some aspects of the known-host case.) Our interest is in decoders that produce reliable estimates whenever the channel is not too severe, where reliable means ... |

19 |
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Citation Context ...loped in this paper are well-suited is the backward-compatible upgrading of an existing communication system, an example of which is the so-called hybrid in-band on-channel digital audio broadcasting =-=[5]-=-, [6]. In this application, one would like to simultaneously transmit a digital signal with existing analog (AM and/or FM) commercial broadcast radio without interfering with conventional analog recep... |

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Method and apparatus for embedding authentication information within digital data
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(Show Context)
Citation Context ...ing method is, the higher the robustness that can be achieved. A great many information-embedding algorithms have been proposed [1] in this still emerging field. Some of the earliest proposed methods =-=[8]-=-, [9], [7] employ a quantize-and-replace strategy: after first quantizing the host signal, these systems change the quantization value to embed information. A simple example of such a system is the so... |

13 |
Information theoretic analysis of steganography
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Citation Context ... QIM, and the asymptotic performance limits of coded QIM using information-theoretic analysis. Other emerging information-theoretic results on the digital watermarking problem are developed in, e.g., =-=[14]��-=-�[20]. The specific organization of the paper is as follows. In Section II, we develop two useful equivalent models for the information-embedding problem. In Section III, we classify traditional appro... |

10 |
Tilborg, “Approaching Capacity by Equiprobable Signaling on the Gaussian Channel
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(Show Context)
Citation Context ...y independent of [29]. Thus, the achievable rate is slightly lower than the case where is Gaussian. The entropy power inequality can be used to show that the decrease in achievable rate is bounded by =-=[36]-=- DNR DNR (54) This gap approaches the upper limit of 0.2546 b/dimension as the DNR gets large. For any finite DNR, the gap is smaller. By subtracting the upper bound on the gap (54) from the capacity ... |

6 |
Detecting Electronic Watermarks in Digital Video
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(Show Context)
Citation Context ...en proposed for allowing a copy-once feature in digital video disc recorders [2]. Alternatively, a standards-compliant player could check the watermark before deciding whether or not to play the disc =-=[3]-=-. Other applications include automated monitoring of airplay of advertisements on commercial radio broadcasts. Advertisers can embed a digital watermark within their ads and count the number of times ... |

3 |
Broadcasting data in the FM band by means of adaptive contiguous band insertion and precancelling techniques
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(Show Context)
Citation Context ... in this paper are well-suited is the backward-compatible upgrading of an existing communication system, an example of which is the so-called hybrid in-band on-channel digital audio broadcasting [5], =-=[6]-=-. In this application, one would like to simultaneously transmit a digital signal with existing analog (AM and/or FM) commercial broadcast radio without interfering with conventional analog reception.... |

1 |
Applications of information hiding
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(Show Context)
Citation Context ...thentication of—or detection of tampering with—the host signal. For example, a digital signature could be embedded in a military map. A number of other national security applications are described=-= in [4] and-=- include covert communication, sometimes called “steganography” or low probability of detection communication, and so-called traitor tracing, a version of the digital fingerprinting application de... |