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## The duality between information embedding and source coding with side information and some applications (2001)

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### Other Repositories/Bibliography

Venue: | in Proc. IEEE Int. Symp. Information Theory |

Citations: | 87 - 13 self |

### Citations

12425 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...ted in Fig. 4. Note that the objective functions on the right-hand sides of (10) and (1) are identical, as occurs in the case of the duality between source and channel coding without side information =-=[15]-=-. Condition (11), i.e., and are conditionally independent given , implies (c.f. (6)) which using (7) simplifies (10) to (13) (14) The achievability proof [15] and that used for the information-embeddi... |

1262 |
Noiseless coding of correlated information sources
- Slepian, Wolf
- 1973
(Show Context)
Citation Context ...free Wyner–Ziv coding—the duality is more interesting. The minimum rate required for distortion-free Wyner–Ziv coding follows immediately from an application of the Slepian–Wolf source-coding theorem =-=[29]-=-. In particular, the source can be reproduced exactly at the decoder ( ) if and only if [15, Sec. 14.4] (19) where the underlying density is prescribed by the problem, so no infimum in (19) is require... |

1059 | The rate–distortion function for source coding with side information at the decoder
- Wyner, Ziv
- 1976
(Show Context)
Citation Context ...nnel coding with side information at the encoder [7], and the problem of source coding with side information at the decoder, the most important instance of which is the well-known “Wyner–Ziv” problem =-=[34]-=-. Exploiting this duality, several new results and interesting insights with practical implications are obtained, including several in the context of mixed analog–digital transmission. Fig. 1 depicts ... |

1041 |
Writing on Dirty Paper
- Costa
- 1983
(Show Context)
Citation Context ...r with mean and covariance matrix . 5 The message is embedded into , creating a composite signal such that the mean-square embedding distortion is minimized: . The capacity of this system is given by =-=[14]-=- (22) Costa proves this result in the context of coding for a channel with a random state known at the encoder. Using a convenient super-channel interpretation of information embedding, Chen and Worne... |

496 | Quantization index modulation: A class of provably good methods for digital watermarking and information embedding,”
- Chen, Wornell
- 2001
(Show Context)
Citation Context ...a host signal, and has an increasingly wide array of applications, from digital watermarking, data hiding, and steganography, to backward-compatible digital upgrading of communications infrastructure =-=[7]-=-, [6]. Likewise, source coding with side information has a growing spectrum of applications, ranging from new low-power sensor networks to the upgrading of legacy communications infrastructure [28], [... |

407 | Distributed source coding using syndromes (discus): Design and construction,” Information Theory
- Pradhan, Ramchandran
- 2003
(Show Context)
Citation Context ... Wyner–Ziv bit rate within the encoder (and adjusting the private decoder parameters accordingly), one 14 There has been renewed interest in implementations of Wyner’s construction lately; see, e.g., =-=[26]-=-. 15 Note that implicit in our assumption of a discrete-time source, all such codes we develop use the same bandwidth as the source.BARRON et al.: THE DUALITY BETWEEN INFORMATION EMBEDDING AND SOURCE... |

265 | Information-Theoretic Analysis of Information Hiding,”
- Moulin, J
- 1999
(Show Context)
Citation Context ...is 1 The decoder can also extract W from Y , thereby reconstructing the original host to within distortion d. 2 For watermarking problems, a variety of attack channel models of the form considered in =-=[23]-=-, [7], and [12] are also of particular interest, although we do not consider such channels in this paper. 0018-9448/03$17.00 © 2003 IEEE1160 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 5, M... |

247 | Rate-Distortion Theory.
- Berger
- 1971
(Show Context)
Citation Context ...mation is also known to the encoder. When the side information is also known to the encoder, achievable performance is easily characterized in terms of a familiar conditional rate-distortion function =-=[5]-=-, [21]. When the side information is not also known to the encoder, we have the problem considered by Wyner and Ziv [34]. While we develop dualities associated with both forms of the source-coding pro... |

223 |
Coding for channel with random parameters,” Probl
- Gelfand, Psinker
- 1980
(Show Context)
Citation Context ...chievable rate for communicating a message such that is arbitrarily small and is arbitrarily close to for sufficiently large . The following result is a generalization of that of Gel’fand and Pinsker =-=[20]-=- and Heegard and El Gamal [22], which consider the problem without a distortion constraint. Claim 1: For general distortion measures , the capacity can be expressed in the form where the supremum is t... |

184 |
Recent results in the Shannon Theory,”
- Wyner
- 1974
(Show Context)
Citation Context ...eveloped in [28] for achieving the Wyner–Ziv rate-distortion limit. In the noise-free special case, the information-embedding system we construct is the dual of Wyner’s Slepian–Wolf code construction =-=[32]-=-. Finally, in Section VI, we exploit our results in the development of a new class of layered joint source–channel coding systems from the interconnection of information embedding and Wyner–Ziv subsys... |

154 |
Gamal, “On the capacity of computer memory with defects
- Heegard, El
- 1983
(Show Context)
Citation Context ...ng a message such that is arbitrarily small and is arbitrarily close to for sufficiently large . The following result is a generalization of that of Gel’fand and Pinsker [20] and Heegard and El Gamal =-=[22]-=-, which consider the problem without a distortion constraint. Claim 1: For general distortion measures , the capacity can be expressed in the form where the supremum is taken over all distributions an... |

135 | The Gaussian watermarking game,”
- Cohen, Lapidoth
- 2002
(Show Context)
Citation Context ...r can also extract W from Y , thereby reconstructing the original host to within distortion d. 2 For watermarking problems, a variety of attack channel models of the form considered in [23], [7], and =-=[12]-=- are also of particular interest, although we do not consider such channels in this paper. 0018-9448/03$17.00 © 2003 IEEE1160 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 5, MAY 2003 Fig. 1.... |

133 |
Intentions in Communication,
- Cohen, Morgen, et al.
- 1990
(Show Context)
Citation Context ...t in the absence of a distortion constraint, one cannot do better than (1) with a nonsingular distribution . The same is true with a distortion constraint present. The following proof is due to Cohen =-=[11]-=-. Lemma 2 (Cohen): For a fixed and , Thus, both and are unchanged by switching to the new auxiliary random variable. If, in addition, the following joint distribution between , , and is defined via if... |

118 |
Systematic lossy source/channel coding
- Shamai, Verdu, et al.
- 1998
(Show Context)
Citation Context ...ure [7], [6]. Likewise, source coding with side information has a growing spectrum of applications, ranging from new low-power sensor networks to the upgrading of legacy communications infrastructure =-=[28]-=-, [1]. This paper develops the natural duality between information embedding, which can be reinterpreted as a problem of channel coding with side information at the encoder [7], and the problem of sou... |

111 | On lattice quantization noise
- Zamir, Feder
- 1996
(Show Context)
Citation Context ...or ), we have the following properties. 7 (GQ-1) The quantization error (30) is white and Gaussian with zero mean and variance , and independent of (29), the codeword to which the vector is quantized =-=[35]-=-. (GQ-2) For every , the probability of a decoding error, when and is a zero-mean white Gaussian vector independent of whose elements have variance [13]. (GQ-3) For all , [35]. We make use of two good... |

90 | Duality between channel capacity and rate distortion with two-sided state information
- Cover, Chiang
- 2002
(Show Context)
Citation Context ... and an expanding set of results and insights. Su, Eggers, and Girod [30] consider the Gaussian-quadratic special case and have a similar geometric interpretation to ours. Chiang and Cover [9], [17], =-=[16]-=- expand the scope of the duality beyond the information-embedding context. Chou, Pradhan, and Ramchandran describe aspects of the duality in [10] and investigate it further in [24], [25]. An outline o... |

53 | Capacity and lattice-strategies for cancelling known interference
- Erez, Shamai
- 2005
(Show Context)
Citation Context ...stic information-embedding systems based on nested lattices that achieve capacity at high signal-to-distortion ratio (SDR). Such systems are also developed independently by Erez, Shamai, and Zamir in =-=[18]-=-. We show how the resulting encoder–decoder pair 3 Throughout this paper it will be clear through context whether a variable to which we refer corresponds to the information-embedding problem or the W... |

40 |
Design and analysis of digital watermarking, informationembedding, and data hiding systems,”
- Chen
- 2000
(Show Context)
Citation Context ...t signal, and has an increasingly wide array of applications, from digital watermarking, data hiding, and steganography, to backward-compatible digital upgrading of communications infrastructure [7], =-=[6]-=-. Likewise, source coding with side information has a growing spectrum of applications, ranging from new low-power sensor networks to the upgrading of legacy communications infrastructure [28], [1]. T... |

40 | Nested linear/lattice codes for Wyner-Ziv encoding,”
- Zamir, Shamai
(Show Context)
Citation Context ...ystem based a nested lattices, which achieves the rate-distortion limit at high signal-to-noise ratio (SNR), and which is a nondithered version of the Wyner–Ziv solution developed by Zamir and Shamai =-=[36]-=-. We further develop, in Appendix III, a Wyner–Ziv code based on nested lattices with dithering that achieves the rate-distortion limit at any SNR. Section V examines the duality further in the case o... |

37 | On the duality between distributed source coding and data hiding
- Chou, Pradhan, et al.
- 1999
(Show Context)
Citation Context ...ic interpretation to ours. Chiang and Cover [9], [17], [16] expand the scope of the duality beyond the information-embedding context. Chou, Pradhan, and Ramchandran describe aspects of the duality in =-=[10]-=- and investigate it further in [24], [25]. An outline of the paper is as follows. After establishing some basic notation in Section II, we develop and relate the basic single-letter characterizations ... |

32 | Lattice quantization with side information
- Servetto
- 2000
(Show Context)
Citation Context ...fectively treated as Gaussian with the indicated variance is also justified by more formal treatment of the underlying limits, as shown in [19]. 10 Such constructions are explored further by Servetto =-=[27]-=-.BARRON et al.: THE DUALITY BETWEEN INFORMATION EMBEDDING AND SOURCE CODING 1167 as the information-embedding decoder (respectively, encoder). It suffices to restrict our attention to the case . For ... |

11 |
Duality of channel capacity and rate distortion with side information
- Chiang, Cover
- 2000
(Show Context)
Citation Context ...cent times, and an expanding set of results and insights. Su, Eggers, and Girod [30] consider the Gaussian-quadratic special case and have a similar geometric interpretation to ours. Chiang and Cover =-=[9]-=-, [17], [16] expand the scope of the duality beyond the information-embedding context. Chou, Pradhan, and Ramchandran describe aspects of the duality in [10] and investigate it further in [24], [25]. ... |

11 |
Coding Theorems of Information Theory, 2nd ed
- Wolfowitz
- 1964
(Show Context)
Citation Context ...he embedding given a particular transmission channel? The dashed line in Fig. 1 represents a less interesting variant of information embedding whereby the host is also known to the decoder. Wolfowitz =-=[31]-=- originally derived capacity for this system without the distortion constraint, i.e., capacity with side information at the encoder and decoder. For the purposes of this 1 The decoder can also extract... |

10 | Illustration of the duality between channel coding and rate distortion with side information
- Su, Eggers, et al.
- 2000
(Show Context)
Citation Context ...In addition to our own work [1], [6], [2], there has been growing interest in aspects of the subject of this paper in recent times, and an expanding set of results and insights. Su, Eggers, and Girod =-=[30]-=- consider the Gaussian-quadratic special case and have a similar geometric interpretation to ours. Chiang and Cover [9], [17], [16] expand the scope of the duality beyond the information-embedding con... |

7 |
rate-distortion function for source coding with side information at the decoder
- “The
- 1976
(Show Context)
Citation Context ...ion embedding capacity with Gaussian host and Gaussian channel. For jointly Gaussian and whose element pairs are all drawn i.i.d. from the Gaussian density , the Wyner–Ziv rate distortion function is =-=[33]-=- if if (23) where is the error variance in the minimum mean-square error (MMSE) estimation of from . We can always write the relationship between and in the form for some , where is Gaussian with vari... |

6 |
Systematic hybrid analog/digital signal coding
- Barron
- 2000
(Show Context)
Citation Context ...], [6]. Likewise, source coding with side information has a growing spectrum of applications, ranging from new low-power sensor networks to the upgrading of legacy communications infrastructure [28], =-=[1]-=-. This paper develops the natural duality between information embedding, which can be reinterpreted as a problem of channel coding with side information at the encoder [7], and the problem of source c... |

6 |
Conditional rate-distortion theory,” Stanford Univ
- Gray
- 1972
(Show Context)
Citation Context ...n is also known to the encoder. When the side information is also known to the encoder, achievable performance is easily characterized in terms of a familiar conditional rate-distortion function [5], =-=[21]-=-. When the side information is not also known to the encoder, we have the problem considered by Wyner and Ziv [34]. While we develop dualities associated with both forms of the source-coding problem, ... |

1 | Signal processing for hybrid channels - Barron, Oppenheim - 1999 |

1 | systematic hybrid analog/digital audio coder - “A - 1999 |

1 |
Lattice decoding can achieve log(1 + SNR) on the AWGN channel using nested codes
- Erez, Zamir
(Show Context)
Citation Context ...roperties are true only in the asymptotic sense, which makes them somewhat hypothetical for any n. See [18] for a more rigorous treatment. 8 The existence of pairs of good nested lattices is shown in =-=[19]-=-, [37]. with (36) where is another parameter. The associated decoder produces the message estimate as the index of the closest coset to its observation , i.e., . We first verify that the embedding rat... |

1 |
Duality between channel and source coding with side information
- Pradhan, Chou, et al.
- 2001
(Show Context)
Citation Context ...nd Cover [9], [17], [16] expand the scope of the duality beyond the information-embedding context. Chou, Pradhan, and Ramchandran describe aspects of the duality in [10] and investigate it further in =-=[24]-=-, [25]. An outline of the paper is as follows. After establishing some basic notation in Section II, we develop and relate the basic single-letter characterizations for the two problems in Section III... |

1 |
characterization of functional duality between source and channel coding
- “A
- 2002
(Show Context)
Citation Context ...er [9], [17], [16] expand the scope of the duality beyond the information-embedding context. Chou, Pradhan, and Ramchandran describe aspects of the duality in [10] and investigate it further in [24], =-=[25]-=-. An outline of the paper is as follows. After establishing some basic notation in Section II, we develop and relate the basic single-letter characterizations for the two problems in Section III. For ... |

1 |
Nested linear/lattice codes for multiterminal binning
- Zamir, Shamai
- 2002
(Show Context)
Citation Context ...ies are true only in the asymptotic sense, which makes them somewhat hypothetical for any n. See [18] for a more rigorous treatment. 8 The existence of pairs of good nested lattices is shown in [19], =-=[37]-=-. with (36) where is another parameter. The associated decoder produces the message estimate as the index of the closest coset to its observation , i.e., . We first verify that the embedding rate is a... |