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Cover-free codes and separating system codes

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Abstract

We give some relations between the asymptotic rates of cover-free (CF) codes, separating system (SS) codes and completely separating system (CSS) codes. We also provide new upper bounds on the asymptotic rate of SS codes based on known results for CF and CSS codes. Finally, we derive a random coding bound for the asymptotic rate of SS codes and give tables of numerical values corresponding to our improved upper bounds.

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References

  1. Barg A., Blakley G.R., Kabatiansky G.A.: Digital fingerprinting codes: problem statements, constructions, identification of traitors. IEEE Trans. Inf. Theory 49(5), 852–865 (2003).

  2. Boneh D., Shaw J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44(5), 1897–1905 (1998).

  3. Cohen G.D., Schaathun H.G.: Asymptotic overview on separating codes. Technical Report 248, Department of Informatics, University of Bergen, Norway (2003).

  4. D’yachkov A.G., Macula A.J., Vilenkin P.A., Torney D.C.: Families of finite sets in which no intersection of \({\ell }\) sets is covered by the union of \(s\) others. J. Comb. Theory Ser. A 99(2), 195–218 (2002).

  5. D’yachkov A.G., Vorobyev I.V., Polyanskii N.A., Shchukin VYu: Bounds on the rate of disjunctive codes. Probl. Inf. Transm. 50(1), 27–56 (2014).

  6. D’yachkov A.G., Vorobyev I.V., Polyanskii N.A., Shchukin V.Yu.: Cover-free codes and separating system codes. In: Proceedings of the IEEE International Symposium on Information Theory (ISIT), pp. 2894–2898, IEEE, Hong Kong (2015).

  7. Engel K.: Interval packing and covering in the Boolean lattice. Comb. Prob. Comput. 5(4), 373–384 (1996).

  8. Friedman A.D., Graham R.L., Ullman J.D.: Universal single transition time asynchronous state assignments. IEEE Trans. Comput. 18(6), 541–547 (1969).

  9. Lebedev V.S.: Asymptotic upper bound for the rate of \((w, r)\) cover-free codes. Probl. Inf. Transm. 39(4), 317–323 (2003).

  10. Mago G.: Monotone functions in sequential circuits. IEEE Trans. Comput. 22(10), 928–933 (1973).

  11. Mitchell C.J., Piper F.C.: Key storage in secure networks. Discret. Appl. Math. 21(3), 215–228 (1988).

  12. Sagalovich Yu.L.: Cascade codes of automata states. Probl. Inf. Transm. 14(2), 77–85 (1978).

  13. Sagalovich Yu.L.: Completely separating systems. Probl. Inf. Transm. 18(2), 140–146 (1982).

  14. Sagalovich Yu.L.: Separating systems. Probl. Inf. Transm. 30(2), 105–123 (1994).

  15. Shangguan C., Wang X., Ge G., Miao Y.: New bounds for frameproof codes, preprint, 2014. arxiv:1411.5782v1

  16. Staddon J.N., Stinson D.R., Wei R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47(3), 1042–1049 (2001).

  17. Stinson D.R., Wei R., Chen K.: On generalized separating hash families. J. Comb. Theory Ser. A 115(1), 105–120 (2008).

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Acknowledgments

I.V. Vorobyev, N.A. Polyanskii and V.Yu. Shchukin have been supported in part by the Russian Science Foundation under Grant No. 14-50-00150.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119992, Moscow, Russian Federation

    A. G. D’yachkov, I. V. Vorobyev, N. A. Polyanskii & V. Yu. Shchukin

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, 127051, Moscow, Russian Federation

    I. V. Vorobyev, N. A. Polyanskii & V. Yu. Shchukin

Authors
  1. A. G. D’yachkov
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  2. I. V. Vorobyev
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  3. N. A. Polyanskii
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  4. V. Yu. Shchukin
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Corresponding authors

Correspondence to A. G. D’yachkov or I. V. Vorobyev.

Additional information

The material in this work was presented in part at the 2015 IEEE International Symposium on Information Theory [6]. This paper contains some improvements of the results, which were developed in [6] (refer to Theorem 2, Theorem 3 and Statement 3 in Theorem 4).

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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D’yachkov, A.G., Vorobyev, I.V., Polyanskii, N.A. et al. Cover-free codes and separating system codes. Des. Codes Cryptogr. 82, 197–209 (2017). https://doi.org/10.1007/s10623-016-0265-9

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  • DOI: https://doi.org/10.1007/s10623-016-0265-9

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