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Signature codes for weighted noisy adder channel, multimedia fingerprinting and compressed sensing

Abstract

We propose a new approach to construct noise-resistant multimedia fingerprinting codes. Our approach is based on the theory of the signature codes for multiple access channels, mainly, for a weighted noisy adder channel. The corresponding multimedia fingerprinting codes allow to trace the entire coalition of pirates. The codes provide significantly better rate than previously known multimedia fingerprinting schemes. We establish the relationship between multimedia fingerprinting and compressed sensing problems.

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References

  1. 1.

    Alon N., Asodi V.: Tracing many users with almost no rate penalty. IEEE Trans. Inf. Theory 53(1), 437–439 (2007).

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Barg A., Blakley G.R., Kabatiansky G.: Digital fingerprinting codes: problems statements, constructions, identification of traitors. IEEE Trans. Inf. Theory 49(4), 852–865 (2003).

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

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

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Candes E.J., Tao T.: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(4), 5406–5425 (2006).

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Chang S.C., Wolf J.K.: On the T-user M-frequency noiseless multiple-access channel with and without intensity information. IEEE Trans. Inf. Theory 27(1), 41–48 (1981).

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Cheng M., Miao Y.: On anti-collusion codes and detection algrithms for multimedia fingerprinting. IEEE Trans. Inf. Theory 57(7), 4843–4851 (2011).

    Article  MATH  Google Scholar 

  7. 7.

    Cheng M., Ji L., Miao Y.: Separable codes. IEEE Trans. Inf. Theory 58(3), 1791–1803 (2012).

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Cheng M., Fu H.-L., Jiang J., Lo Y.-H., Miao Y.: New bounds on 2-separable codes of length 2. Des. Codes Cryptogr. 74(3), 31–40 (2015).

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Chor B., Fiat A., Naor M.: Tracing traitors. In: Desmedt Y.G. (ed.) Advances in Cryptology–Crypto’94, LNCS, vol. 839, pp. 480–491. Springer, New York (1994).

    Google Scholar 

  10. 10.

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

  11. 11.

    Collins M.J.: Upper bounds for parent-identifying set systems. Des. Codes Cryptogr. 51(2), 167–173 (2009).

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Csros M., Ruszinko M.: Single-user tracing and disjointly superimposed codes. IEEE Trans. Inf. Theory 51(4), 1606–1611 (2005).

    MathSciNet  Article  MATH  Google Scholar 

  13. 13.

    Donoho D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Egorova E., Fernandez M., Kabatiansky G., Lee M.H.: Signature codes for A-channel and collusion-secure multimedia fingerprinting codes. In: Proceedings 2016 IEEE International Symposium on Information Theory, Barcelona, pp. 3043–3047 (2016).

  15. 15.

    Egorova E., Fernandez M., Kabatiansky G.: Multimedia fingerprinting codes resistant against colluders and noise. In: Proceedings of 8th IEEE International Workshop on Information Forensic and Security, Abu Dhabi, pp. 1–5 (2016).

  16. 16.

    Gao F., Ge G.: New bounds on separable codes for multimedia fingerprinting. IEEE Trans. Inf. Theory 60, 5257–5262 (2014).

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Gritsenko V., Kabatiansky G., Lebedev V., Maevskiy A.: Signature codes for noisy multiple access adder channel. Des. Codes Cryptogr. 82(1), 293–299 (2017).

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Hollmann H.D.L., van Lint J.H., Linnartz J.-P., Tolhuizen L.M.G.M.: On codes with the identifiable parent property. J. Comb. Theory Ser. A 82(2), 121–133 (1998).

    MathSciNet  Article  MATH  Google Scholar 

  19. 19.

    Jiang J., Cheng M., Miao Y.: Strongly separable codes. Des. Codes Cryptogr. 79(2), 303–318 (2016).

    MathSciNet  Article  MATH  Google Scholar 

  20. 20.

    Kabatiansky G., Vladuts S., Tavernier C.: On the doubly sparse compressed sensing problem. In: Proceedings of IMAAC 2015, LNCS, vol. 9496, pp. 1–6 (2015).

  21. 21.

    Kabatiansky G., Lomakov V., Vladuts S.: On codes correcting errors in channel and syndrom. Probl. Inf. Transm. 51(2), 50–57 (2015).

    Google Scholar 

  22. 22.

    Liu K.J.R., Trappe W., Wang Z.J., Wu M., Zhao H.: Multimedia Fingerprinting Forensics for Traitor Tracing, vol. 4. Hindawi Publishing Corporation, Cairo (2005).

    Book  Google Scholar 

  23. 23.

    Mathys P.: A class of codes for a T active users out of N multiple-access communvation system. IEEE Trans. Inf. Theory 36(6), 1206–1219 (1990).

    MathSciNet  Article  MATH  Google Scholar 

  24. 24.

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

  25. 25.

    Stinson D.R., Wei R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM J. Discret. Math. 11(1), 41–53 (1998).

    MathSciNet  Article  MATH  Google Scholar 

  26. 26.

    Tardos G.: Optimal probabilistic fingerprint codes. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, June 9-11, 2003, San Diego, CA, USA, ACM, pp. 116–125 (2003).

  27. 27.

    Trappe W., Wu M., Wang Z.J., Liu K.J.R.: Anti-collusion fingerprinting for multimedia. IEEE Trans. Signal Process. 51, 1069–1087 (2003).

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Elena Egorova.

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

The work of E. Egorova and G. Kabatiansky has been supported by the RFBR Grants 18-07-01427 and 16-01-00716. The work of M. Fernández has been supported by the Spanish Government Grant TEC2015-68734-R and Catalan Government Grant SGR 782.

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Egorova, E., Fernandez, M., Kabatiansky, G. et al. Signature codes for weighted noisy adder channel, multimedia fingerprinting and compressed sensing. Des. Codes Cryptogr. 87, 455–462 (2019). https://doi.org/10.1007/s10623-018-0551-9

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Keywords

  • Multimedia fingerprinting
  • Signature codes for multiple access channels
  • Compressed sensing

Mathematics Subject Classification

  • 94B60