Cesar Bolaños
ABSTRACT
We construct a new family of 3D periodic arrays suitable for water-marking video. Each member of the family is composed of columns of cyclic shifts of a Sidelnikov sequence in which the shifts are given by an m x n "grid" that is determined by applying a logarithmic quadratic map to the elements of a direct product Zm| x Zn. These arrays have peak auto-correlation on the order of p4 and non-peak auto- and cross-correlation on the order of p2 and unlike other constructions have unequal dimensions.
- Rafael Arce-Nazario, Francis Castro, Domingo Gomez-Perez, Oscar Moreno, José Ortiz-Ubarri, Ivelisse Rubio, and Andrew Tirkel. 2020. Multidimensional Linear Complexity Analysis of Periodic Arrays. Appl. Algebra Eng., Commun. Comput. 31, 1 (jan 2020), 43--63. Google Scholar
Digital Library
- Sam Blake, Oscar Moreno, and Andrew Tirkel. 2014. Families of 3D Arrays for Video Watermarking. In Sequences and Their Applications - SETA 2014, Kai-Uwe Schmidt and Arne Winterhof (Eds.), Vol. 8865. Springer, Melbourne, Australia, 134 -- 145. International Conference on Sequences and Their Applications 2014, SETA 2014 ; Conference Date: 24-11-2014 Through 28-11-2014. Google ScholarDigital Library
- Domingo Gomez-Perez, Ana-Isabel Gomez, and Andrew Tirkel. 2017. Arrays Composed from the Extended Rational Cycle. Advances in Mathematics of Communications 11 (05 2017), 313--327. Google ScholarCross Ref
- Oscar Moreno and Andrew Tirkel. 2011. Multi-dimensional Arrays for Watermarking. In 2011 IEEE International Symposium on Information Theory Proceedings. St. Petersburg, Rusia, 2691 -- 2695. Google ScholarCross Ref
- Oscar Moreno and Andrew Tirkel. 2012. New Optimal Low Correlation Sequences for Wireless Communications. In Proceedings of the 7th International Conference on Sequences and Their Applications. Springer-Verlag, Berlin, Heidelberg, 212--223. Google ScholarDigital Library
- Kenneth Rosen. 2010. Handbook of Discrete and Combinatorial Mathematics, Second Edition (2nd ed.). Chapman & Hall/CRC.Google Scholar
- Vladimir Michilovich Sidelnikov. 1969. Some k-Valued Pseudo-random Sequences and Nearly Equidistant Codes. Problemy Peredachi Informatsii 5, 1 (1969), 16--22.Google Scholar
Index Terms
- A new family of 3D watermarks
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