## Scalar Costa Scheme for Information Embedding (2002)

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Venue: | IEEE Transactions on Signal Processing |

Citations: | 89 - 1 self |

### BibTeX

@ARTICLE{Eggers02scalarcosta,

author = {Joachim J. Eggers and Robert Bäuml and Roman Tzschoppe and Bernd Girod},

title = {Scalar Costa Scheme for Information Embedding},

journal = {IEEE Transactions on Signal Processing},

year = {2002},

volume = {51},

pages = {1003--1019}

}

### Years of Citing Articles

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### Abstract

Research on information embedding and particularly information hiding techniques has received considerable attention within the last years due to its potential application in multimedia security. Digital watermarking, which is an information hiding technique where the embedded information is robust against malicious or accidental attacks, might offer new possibilities to enforce the copyrights of multimedia data. In this article, the specific case of information embedding into independent identically distributed (IID) data and attacks by additive white Gaussian noise (AWGN) is considered. The original data is not available to the decoder. For Gaussian data, Costa proposed already in 1983 a scheme that theoretically achieves the capacity of this communication scenario. However, Costa's scheme is not practical. Thus, several research groups have proposed suboptimal practical communication schemes based on Costa's idea. The goal of this artical is to give a complete performance analysis of the scalar Costa scheme (SCS) which is a suboptimal technique using scalar embedding and reception functions. Information theoretic bounds and simulation results with state-of-the-art coding techniques are compared. Further, reception after amplitude scaling attacks and the invertibility of SCS embedding are investigated. Keywords Information embedding, communication with side-information, blind digital watermarking, scalar Costa scheme I.

### Citations

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Citation Context ...age is encoded such that for each data element an �� ¨����������������� alphabet� � of watermark letters is used, where each letter is equiprobable. Then the=-= mutual information��� ���� is �� given by [30] ��� ���� ¨ � � �� ����������¤�� ��������� It can be that��� obser-=-ved ����is completely determined by PDFs��� the in Sec. III-B for the case of AWGN attacks. ������and��� � � � ����� � (20) � �� �����... |

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Citation Context ... a statistically independent pseudo-noise signal§ with power is derived from the watermark message¡ and the key� . SS watermarking is one of the which first methods used for watermarking (e.g., [3=-=1], [32]) and is still the most po-=-pular one. For a Gaussian original signal, AWGN attack, and for a Gaussian watermark signal � £¤� ���£¤���the capacity of blind ���sIEEE TRANSACTIONS ON SIGNAL PROCESSING, VO... |

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Citation Context ...cKIEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 3 ellips [8]. Chen and Wornell introduced an important but almost forgotten paper by Costa into the watermarking community. Costa [=-=9] showe-=-d theoretically that the channel capacity for the communication scenario depicted in Fig. 1 with an IID Gaussian host signal¢ is independent ¥.The suffix “ICS” stands for ideal Costa scheme, and... |

680 | Quantization
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Citation Context ...e quantizer input¢ for an almost uniform original data PDF in the range of one quantization bin. For the given codebook encryption by a uniformly distributed key sequence�, it can even be shown [24=-=], [25] and§ are statistically -=-independent from¢, as it is in Costa’s ideal scheme. Further, the power of the quantization error is that� always for the given distribution of the key sequence. ¤��� ¨ E���¤��... |

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Citation Context ... over ST-DM in the range of negative ����� s. C. SCS with State-of-the-Art Channel Coding Repetition coding is known to be very inefficient. State-of-the-art error correction codes, e.g., tu=-=rbo codes [36], outperform repetit-=-ion coding by far. Therefore, simulation results for SCS communication using turbo coding are presented in Fig. 15. Fig. 15 shows the minimum ������� ��� for which coded SCS waterm... |

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Citation Context ... their efficient combination � with binary coding � techniques. -ary signaling is used for the classical trellis coded modulation with � with� convolutional codes (CC-TCM) as proposed by Unger=-=boeck � [35]-=-. -ary signaling is used in combination with a new trellis coded modulation scheme with serial concatenated codes and iterative decoding (SC-TCM). A detailed discussion of coded modulation is beyond t... |

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Citation Context ...tizers. Then, DM can be considered where� a special case of SCS, regardless of the . is optimized in SCS for (see Sec. III-C), SCS can never perform worse than ¨ each����� Since� � ��=-=����� DM. In [11], [27], Ch-=-en and Wornell discuss the extension of QIM using Costa’s ideas, and denote the derived scheme as QIM with distortion compensation which is basically Costa’s scheme described in a different way. I... |

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Citation Context ...led areas represent the probability of decision errors assuming����� ,� ,� was transmitted. C. Capacity Computation and Optimum SCS Step Size For the discrete memoryless channel, Gel’f=-=and and Pinsker [28] and Heegard and El Gamal [-=-29] showed that, for communication with side information at the encoder, the capacity is given by where the maximum is taken over all joint PDFs form�¥ ��������� of the ���a... |

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Citation Context ...NAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 2 data, but watermarking of audio and video data is popular as well. Theoretical limits of digital watermarking have been investigated since about 1999 [1], =-=[2]-=-, [3]. In general, watermark embedding techniques and attacks against watermarks have to be designed specifically for certain host data types. A particularly interesting case is that of independent id... |

231 |
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Citation Context ...ing techniques can be shown in future. Note also that principles of Costa’s work on communication with side information have recently gained some attention within multiuser communications [20], [21]=-=, [22]-=-. The goal of this paper is to summarize theoretical and experimental results on the performance of the practical SCS embedding and reception technique. An accurate performance analysis is based on pr... |

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Citation Context ... with side-information at the encoder. This has been first realized in 1999 by Chen and Wornell [7] and Cox, Miller and McKIEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 3 ellips [=-=8]-=-. Chen and Wornell introduced an important but almost forgotten paper by Costa into the watermarking community. Costa [9] showed theoretically that the channel capacity for the communication scenario ... |

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Citation Context ...possible received signal. This is indicated by the dotted line in the lower plot of Fig. 5. C. Capacity Computation and Optimum SCS Step Size For the discrete memoryless channel, Gel’fand and Pinsker =-=[28]-=- and Heegard and El Gamal [29] showed that for communication with side information at the encoder, the capacity is given by (18) where the maximum is taken over all joint PDFs of the form x r and wher... |

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Citation Context ...ility of decision errors assuming����� ,� ,� was transmitted. C. Capacity Computation and Optimum SCS Step Size For the discrete memoryless channel, Gel’fand and Pinsker [28] and Heega=-=rd and El Gamal [29] showed that, for communication with side informa-=-tion at the encoder, the capacity is given by where the maximum is taken over all joint PDFs form�¥ ��������� of the ���and ���������� �, respectively.... |

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Citation Context ...t certain versions of the technique proposed by Ramkumar and Akansu show good performance particularly for very s. low����� SCS outperforms their approach in the range of typical����=-=� s only slightly [17]-=-. Chou et al. [18] exploit the duality of communication with side-information at the encoder to source coding with side-information at the decoder to derive a watermarking scheme based on trellis-code... |

48 |
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Citation Context ...mplementation of Costa’s scheme. Chen and Wornell developed in 1998 quantization index modulation (QIM) which provides good performance for low channel noise, but is not robust for channel condition=-=s [10], £¤� with-=-£¤��� [1]. In 1999, they improved the QIM idea using Costa’s approach and named the new scheme QIM with distortion compensation (DC-QIM) [11]. Most of the work of Chen and Wornell concentrat... |

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Citation Context ...ion of a statistically independent pseudo-noise signal§ with power is derived from the watermark message¡ and the key� . SS watermarking is one of the which first methods used for watermarking (e.=-=g., [31], [32]) and is still the m-=-ost popular one. For a Gaussian original signal, AWGN attack, and for a Gaussian watermark signal � £¤� ���£¤���the capacity of blind ���sIEEE TRANSACTIONS ON SIGNAL PROCESSI... |

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Citation Context ...ional embedding techniques can be shown in future. Note also that principles of Costa’s work on communication with side information have recently gained some attention within multiuser communication=-=s [20]-=-, [21], [22]. The goal of this paper is to summarize theoretical and experimental results on the performance of the practical SCS embedding and reception technique. An accurate performance analysis is... |

40 |
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Citation Context ...codes, can be used to decode from� the most likely transmitted message� watermark . C. Quantization Index Modulation and Dither Modulation ¡ Quantization index modulation (QIM), as described in [=-=10], [26] is a-=- special case of Costa’s scheme, regardless of . As a result, QIM can achieve the capacity of ICS as tends to infinity. However, which is relevant in watermarking applications, reliable commu¨ £¤... |

37 |
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Citation Context ... to the quantizer input¢ for an almost uniform original data PDF in the range of one quantization bin. For the given codebook encryption by a uniformly distributed key sequence�, it can even be sho=-=wn [24], [25] and§ a-=-re statistically independent from¢, as it is in Costa’s ideal scheme. Further, the power of the quantization error is that� always for the given distribution of the key sequence. ¤��� ¨ E... |

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Citation Context ... noise, but is not robust for channel conditions [10], £¤� with£¤��� [1]. In 1999, they improved the QIM idea using Costa’s approach and named the new scheme QIM with distortion compensa=-=tion (DC-QIM) [11]-=-. Most of the work of Chen and Wornell concentrates on high (3)sIEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 4 dimensional embedding techniques where the dimensionality tends to ... |

35 |
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Citation Context ...-RATE SCS COMMUNICATION is slightly steeper than High-rate SCS communication is of interest for scenarios with low attack noise, for instance, if information embedding into analog channels is desired =-=[33], [27], -=-[34]. Here, information embedding at rates � bit/element is considered high-rate watermarking, since for these rates the capacity of binary SCS is significantly lower for� than -ary with� �, s... |

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(Show Context)
Citation Context ...ROCESSING, VOL. XX, NO. Y, MONTH 2002 2 data, but watermarking of audio and video data is popular as well. Theoretical limits of digital watermarking have been investigated since about 1999 [1], [2], =-=[3]-=-. In general, watermark embedding techniques and attacks against watermarks have to be designed specifically for certain host data types. A particularly interesting case is that of independent identic... |

28 | Provably robust digital watermarking
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(Show Context)
Citation Context ...N SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 2 data, but watermarking of audio and video data is popular as well. Theoretical limits of digital watermarking have been investigated since about 1999 =-=[1]-=-, [2], [3]. In general, watermark embedding techniques and attacks against watermarks have to be designed specifically for certain host data types. A particularly interesting case is that of independe... |

27 | A robust optimization solution to the data hiding problem using distributed source coding principles
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- 2000
(Show Context)
Citation Context ... of the technique proposed by Ramkumar and Akansu show good performance particularly for very s. low����� SCS outperforms their approach in the range of typical����� s only slightl=-=y [17]. Chou et al. [18]-=- exploit the duality of communication with side-information at the encoder to source coding with side-information at the decoder to derive a watermarking scheme based on trellis-coded quantization. Th... |

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- Chen, W
- 1999
(Show Context)
Citation Context ...tion facing an AWGN attack Watermark communication as shown in Fig. 1 can be considered as communication with side-information at the encoder. This has been first realized in 1999 by Chen and Wornell =-=[7-=-] and Cox, Miller and McKIEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 2002 3 ellips [8]. Chen and Wornell introduced an important but almost forgotten paper by Costa into the watermar... |

21 |
Data Hiding in Multimedia -- Theory and Applications
- Ramkumar
- 1999
(Show Context)
Citation Context ...se. However, the specific shape of the involved PDFs of the transmitted and received signals are not modelled accurately so that tight performance limits cannot be computed. Ramkumar and Akansu [12], =-=[13]-=-, [14], [15], [16] propose a blind watermarking technique based on periodic embedding and reception functions for self-noise suppression (host signal interference reduction). In particular low dimensi... |

17 | Performance of a practical blind watermarking scheme
- Eggers, Su, et al.
- 2001
(Show Context)
Citation Context ... that of independent identically distributed (IID) host data and attacks by additive white Gaussian noise (AWGN). The analysis of more complicated scenarios can often be ascribed to this special case =-=[4]-=-, [5], [6]. In this paper, we focus on information embedding into IID host data facing AWGN attacks. Throughout the paper, we denote the investigated scenario as a watermarking scenario. However, it s... |

16 | Estimation of amplitude modifications before SCS watermark detection
- Eggers, Bäuml, et al.
- 2002
(Show Context)
Citation Context ...essage with different possible step sizes. Finally, we discuss here a specific step size estimation algorithm which is based on the analysis of histrograms of received data � with SCS watermarks [5]=-=, [37]. Fig. 16 depicts an extension of Fig. 1 where-=- the attacker scales the watermarked data � by � (usually � ) and introduces additive white Gaussian noise (AWGN) � , ��� ���¥¤§¦©¨��� with ¢¡£ . ����� , ... |

14 | Akansu, “Self-noise suppression schemes in blind image steganography
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- 1999
(Show Context)
Citation Context ...ck noise. However, the specific shape of the involved PDFs of the transmitted and received signals are not modelled accurately so that tight performance limits cannot be computed. Ramkumar and Akansu =-=[12]-=-, [13], [14], [15], [16] propose a blind watermarking technique based on periodic embedding and reception functions for self-noise suppression (host signal interference reduction). In particular low d... |

14 |
Turbo coded trellis-based constructions for data embedding: Channel coding with side information
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- 2001
(Show Context)
Citation Context ...en made within the last years. Up to now, performance results that are better than the theoretical capacity limit of ST-SCS propose (see Sec. V) have not been published. Latest results by Chou et al. =-=[19]-=- show at least a slight improvement of turbo coded trellisbased constructions over simple SCS communication using coded modulation techniques. Note also thatsIEEE TRANSACTIONS ON SIGNAL PROCESSING, VO... |

13 | Trusted headers for medical images
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- 1999
(Show Context)
Citation Context ... SCS In some applications, it is desired to recover the original signal from the watermarked signal after watermark reception. Examples are information hiding applications dealing with medical images =-=[38]-=-, or multiple watermark reception. In applications dealing with medical images, the goal is mainly to recover the original signal with a minimum amount of distortion. In multiple watermark reception, ... |

11 | uantization watermarking, in - Eggers, Girod |

8 |
Information Embedding and Digital Watermarking as Communication with
- Eggers
- 2001
(Show Context)
Citation Context ... of independent identically distributed (IID) host data and attacks by additive white Gaussian noise (AWGN). The analysis of more complicated scenarios can often be ascribed to this special case [4], =-=[5]-=-, [6]. In this paper, we focus on information embedding into IID host data facing AWGN attacks. Throughout the paper, we denote the investigated scenario as a watermarking scenario. However, it should... |

6 | Floating Signal Constellations for Multimedia Steganography
- Ramkumar, Akansu, et al.
- 2000
(Show Context)
Citation Context ... the specific shape of the involved PDFs of the transmitted and received signals are not modelled accurately so that tight performance limits cannot be computed. Ramkumar and Akansu [12], [13], [14], =-=[15]-=-, [16] propose a blind watermarking technique based on periodic embedding and reception functions for self-noise suppression (host signal interference reduction). In particular low dimensional version... |

6 | 2001) “Next generation techniques for robust and imperceptible audio data hiding
- Chou, Ramchandrad
(Show Context)
Citation Context ...MMUNICATION is slightly steeper than High-rate SCS communication is of interest for scenarios with low attack noise, for instance, if information embedding into analog channels is desired [33], [27], =-=[34]. Here, -=-information embedding at rates � bit/element is considered high-rate watermarking, since for these rates the capacity of binary SCS is significantly lower for� than -ary with� �, signaling as ... |

1 | FFT based signaling for multimedia steganography
- Ramkumar, Akansu
- 2000
(Show Context)
Citation Context ...wever, the specific shape of the involved PDFs of the transmitted and received signals are not modelled accurately so that tight performance limits cannot be computed. Ramkumar and Akansu [12], [13], =-=[14]-=-, [15], [16] propose a blind watermarking technique based on periodic embedding and reception functions for self-noise suppression (host signal interference reduction). In particular low dimensional v... |

1 |
Periodic signaling scheme in oblivious data hiding
- Gang, Akansu, et al.
- 2000
(Show Context)
Citation Context ...pecific shape of the involved PDFs of the transmitted and received signals are not modelled accurately so that tight performance limits cannot be computed. Ramkumar and Akansu [12], [13], [14], [15], =-=[16]-=- propose a blind watermarking technique based on periodic embedding and reception functions for self-noise suppression (host signal interference reduction). In particular low dimensional versions of t... |

1 |
Applying the dirty paper approach to the downlink of a cellular system
- Shamai, Zaidel
(Show Context)
Citation Context ...embedding techniques can be shown in future. Note also that principles of Costa’s work on communication with side information have recently gained some attention within multiuser communications [20]=-=, [21]-=-, [22]. The goal of this paper is to summarize theoretical and experimental results on the performance of the practical SCS embedding and reception technique. An accurate performance analysis is based... |