On joint information embedding and lossy compression in the presence of a stationary memoryless attack channel

We consider the problem of optimum joint public information embedding and lossy compression with respect to a fidelity criterion. The decompressed composite sequence (stegotext) is distorted by a stationary memoryless attack, resulting in a forgery which in turn is fed into the decoder, whose task is to retrieve the embedded information. The goal of this paper is to characterize the maximum achievable embedding rate R/sub e/ (the embedding capacity C/sub e/) as a function of the compression (composite) rate R/sub c/ and the allowed average distortion level /spl Delta/, such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length. We characterize the embedding capacity and demonstrate how it can be approached in principle. We also provide a single-letter expression of the minimum achievable composite rate as a function of R/sub e/ and /spl Delta/, below which there exists no reliable embedding scheme.

[1]  Neri Merhav On random coding error exponents of watermarking systems , 2000, IEEE Trans. Inf. Theory.

[2]  Marten van Dijk,et al.  Capacity and codes for embedding information in gray-scale signals , 2005, IEEE Transactions on Information Theory.

[3]  Damianos Karakos Digital Watermarking, Fingerprinting and Compression: An Information-Theoretic Perspective , 2002 .

[4]  Edward J. Delp,et al.  Watermark embedding: hiding a signal within a cover image , 2001, IEEE Commun. Mag..

[5]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[6]  Damianos Karakos,et al.  A relationship between quantization and watermarking rates in the presence of additive Gaussian attacks , 2003, IEEE Trans. Inf. Theory.

[7]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for multimedia , 1997, IEEE Trans. Image Process..

[8]  Ross J. Anderson,et al.  On the limits of steganography , 1998, IEEE J. Sel. Areas Commun..

[9]  Oleh John Tretiak Rate Distortion Theory: A Mathematical Basis for Data Compression, Toby Berger. Prentice-Hall, Urbana, IL (1971) , 1974 .

[10]  Claude E. Shannon,et al.  Channels with Side Information at the Transmitter , 1958, IBM J. Res. Dev..

[11]  Neri Merhav,et al.  On the capacity game of public watermarking systems , 2004, IEEE Transactions on Information Theory.

[12]  Joseph A. O'Sullivan,et al.  Information-theoretic analysis of information hiding , 2003, IEEE Trans. Inf. Theory.

[13]  N. Merhav,et al.  On joint information embedding and lossy compression in the presence of a stationary memoryless attack channel , 2004 .

[14]  Neri Merhav,et al.  On joint information embedding and lossy compression , 2005, IEEE Transactions on Information Theory.

[15]  Markus G. Kuhn,et al.  Information hiding-a survey , 1999, Proc. IEEE.

[16]  Ingemar J. Cox,et al.  Watermarking as communications with side information , 1999, Proc. IEEE.

[17]  Toby Berger,et al.  Rate distortion theory : a mathematical basis for data compression , 1971 .

[18]  T. Berger Rate-Distortion Theory , 2003 .

[19]  Amos Lapidoth,et al.  The Gaussian watermarking game , 2000, IEEE Trans. Inf. Theory.

[20]  Neri Merhav,et al.  On the error exponent and capacity games of private watermarking systems , 2003, IEEE Trans. Inf. Theory.

[21]  Ahmed H. Tewfik,et al.  Multimedia data-embedding and watermarking technologies , 1998, Proc. IEEE.

[22]  E. Yang,et al.  Joint watermarking and compression using scalar quantization for maximizing robustness in the presence of additive Gaussian attacks , 2005 .

[23]  Damianos Karakos,et al.  A Relationship between Quantization and Distribution Rates of Digitally Fingerprinted Data , 2000 .

[24]  Gregory W. Wornell,et al.  The duality between information embedding and source coding with side information and some applications , 2003, IEEE Trans. Inf. Theory.

[25]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[26]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[27]  Gregory W. Wornell,et al.  Quantization index modulation: A class of provably good methods for digital watermarking and information embedding , 2001, IEEE Trans. Inf. Theory.