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Construction of Perfect Auto-correlation Arrays and Zero Cross-correlation Arrays from Discrete Projections

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Combinatorial Image Analysis (IWCIA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9448))

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Abstract

This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.

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Acknowledgements

The authors thank Andrew Tirkel for sharing his expertise on sequences and the generation of perfect auto-correlation arrays. BC acknowledges support from Polytech Nantes and the School of Physics and Astronomy, Monash University as hosts for his internship.

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Authors and Affiliations

  1. Polytech Nantes, University of Nantes, Nantes, France

    Benjamin Cavy

  2. Department of Physics and Astronomy, Monash University, Melbourne, Australia

    Imants Svalbe

Authors
  1. Benjamin Cavy
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  2. Imants Svalbe
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Correspondence to Imants Svalbe .

Editor information

Editors and Affiliations

  1. SUNY Fredonia, Fredonia, New York, USA

    Reneta P. Barneva

  2. Advanced Computing and Microelectronics, Indian Statistical Institute, Kolkata, Germany

    Bhargab B. Bhattacharya

  3. SUNY Buffalo State, Buffalo, New York, USA

    Valentin E. Brimkov

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Cavy, B., Svalbe, I. (2015). Construction of Perfect Auto-correlation Arrays and Zero Cross-correlation Arrays from Discrete Projections. In: Barneva, R., Bhattacharya, B., Brimkov, V. (eds) Combinatorial Image Analysis. IWCIA 2015. Lecture Notes in Computer Science(), vol 9448. Springer, Cham. https://doi.org/10.1007/978-3-319-26145-4_17

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  • DOI: https://doi.org/10.1007/978-3-319-26145-4_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26144-7

  • Online ISBN: 978-3-319-26145-4

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