On random coding error exponents of watermarking systems

Watermarking codes are analyzed from an information-theoretic viewpoint as a game between an information hider and an active attacker. While the information hider embeds a secret message (watermark) in a covertext message (typically: text, image, sound, or video stream) within a certain distortion level, the attacker processes the resulting watermarked message, within limited additional distortion, in attempt to invalidate the watermark. For the case where the covertext source is memoryless (or, more generally where there exists some transformation that makes it memoryless), we provide a single-letter characterization of the maximin game of the random coding error exponent associated with the average probability of erroneously decoding the watermark. This single-letter characterization is in effect because if the information hider utilizes a memoryless channel to generate random codewords for every covertext message, the (causal) attacker will maximize the damage by implementing a memoryless channel as well. Partial results for the dual minimax game and the conditions for the existence of a saddle point are also presented.

[1]  Irvin G. Stiglitz,et al.  Coding for a class of unknown channels , 1966, IEEE Trans. Inf. Theory.

[2]  J.A. O'Sullivan,et al.  Information theoretic analysis of steganography , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[3]  J. Stoer,et al.  Convexity and Optimization in Finite Dimensions I , 1970 .

[4]  Poss Anderson Stretching the Limits of Steganography P ~ oss Anderson , .

[5]  Robert G. Gallager,et al.  The random coding bound is tight for the average code (Corresp.) , 1973, IEEE Trans. Inf. Theory.

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

[7]  Amos Lapidoth,et al.  On the Universality of the LZ-Based Decoding Algorithm , 1998, IEEE Trans. Inf. Theory.

[8]  Evaggelos Geraniotis,et al.  Minimax robust coding for channels with uncertainty statistics , 1985, IEEE Trans. Inf. Theory.

[9]  Neri Merhav Universal decoding for memoryless Gaussian channels with a deterministic interference , 1993, IEEE Trans. Inf. Theory.

[10]  A. Lapidoth,et al.  On the Gaussian watermarking game , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[11]  Irvin G. Stiglitz,et al.  A coding theorem for a class of unknown channels , 1967, IEEE Trans. Inf. Theory.

[12]  Brian L. Hughes,et al.  On error exponents for arbitrarily varying channels , 1996, IEEE Trans. Inf. Theory.

[13]  Thomas H. E. Ericson,et al.  Exponential error bounds for random codes in the arbitrarily varying channel , 1985, IEEE Trans. Inf. Theory.

[14]  Jacob Ziv,et al.  Universal decoding for finite-state channels , 1985, IEEE Trans. Inf. Theory.

[15]  R. Gallager Information Theory and Reliable Communication , 1968 .

[16]  Robert G. Gallager,et al.  A simple derivation of the coding theorem and some applications , 1965, IEEE Trans. Inf. Theory.

[17]  Meir Feder,et al.  Universal Decoding for Channels with Memory , 1998, IEEE Trans. Inf. Theory.

[18]  Ross J. Anderson Stretching the Limits of Steganography , 1996, Information Hiding.

[19]  Kannan Ramchandran,et al.  Capacity issues in digital image watermarking , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[20]  Meir Feder,et al.  Universal decoders for channels with memory , 1996 .