Scalar Quadratic-Gaussian soft watermarking games

M. Kıvanç Mıhçak, Emrah Akyol, Tamer Başar, Cédric Langbort

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We introduce a zero-sum game problem of soft watermarking: The hidden information (watermark) comes from a continuum and has a perceptual value; the receiver generates an estimate of the embedded watermark to minimize the expected estimation error (unlike the conventional watermarking schemes where both the hidden information and the receiver output are from a discrete finite set). Applications include embedding a multimedia content into another. We study here the scalar Gaussian case and use expected mean-squared distortion. We formulate the problem as a zero-sum game between the encoder & receiver pair and the attacker. We show that for linear encoder, the optimal attacker is Gaussian-affine, derive the optimal system parameters in that case, and discuss the corresponding system behavior. We also provide numerical results to gain further insight and understanding of the system behavior at optimality.

Original languageEnglish (US)
Title of host publicationDecision and Game Theory for Security - 7th International Conference, GameSec 2016, Proceedings
EditorsEmmanouil Panaousis, Milind Tambe, Tansu Alpcan, William Casey, Quanyan Zhu
Number of pages20
ISBN (Print)9783319474120
StatePublished - 2016
Event7th International Conference on Decision and Game Theory for Security, GameSec 2016 - New York, United States
Duration: Nov 2 2016Nov 4 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9996 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other7th International Conference on Decision and Game Theory for Security, GameSec 2016
Country/TerritoryUnited States
CityNew York

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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