Advertisement

Problems of Information Transmission

, Volume 55, Issue 2, pp 101–123 | Cite as

Reliable Communication under the Influence of a State-Constrained Jammer: An Information-Theoretic Perspective on Receive Diversity

  • C. ArendtEmail author
  • J. NötzelEmail author
  • H. BocheEmail author
Information Theory

Abstract

The impact of diversity on reliable communication over arbitrarily varying channels (AVC) is investigated as follows. First, the concept of an identical state-constrained jammer is motivated. Second, it is proved that symmetrizability of binary symmetric AVCs (AVBSC) caused by identical state-constrained jamming is circumvented when communication takes place over at least three orthogonal channels. Third, it is proved that the deterministic capacity of the identical state-constrained AVBSC is continuous and shows super-activation. This effect was hitherto demonstrated only for quantum communication and for classical communication under secrecy constraints.

Key words

arbitrarily varying channel unknown interference deterministic coding receive diversity super-activation continuity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgement

The first author would like to thank P. Fertl and A. Posselt from the BMW Group for supporting his studies. Moreover, the authors would like to thank an unknown reviewer for useful comments and detailed examination of the present manuscript.

References

  1. 1.
    Blackwell, D., Breiman, L., and Thomasian, A.J., The Capacities of Certain Channel Classes under Random Coding, Ann. Math. Statist., 1960, vol. 31, no. 3, pp. 558–567.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Lapidoth, A. and Narayan, P., Reliable Communication under Channel Uncertainty, IEEE Trans. Inform. Theory, 1998, vol. 44, no. 6, pp. 2148–2177.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Csiszár, I. and Körner, J., Information Theory: Coding Theorems for Discrete Memoryless Systems, Cambridge: Cambridge Univ. Press, 2011, 2nd ed.CrossRefzbMATHGoogle Scholar
  4. 4.
    Ahlswede, R. and Wolfowitz, J., Correlated Decoding for Channels with Arbitrarily Varying Channel Probability Functions, Inform. Control, 1969, vol. 14, no. 5, pp. 457–473.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Schaefer, R.F., Boche, H., and Poor, H.V., Secure Communication under Channel Uncertainty and Adversarial Attacks, Proc. IEEE, 2015, vol. 103, no. 10, pp. 1796–1813.CrossRefGoogle Scholar
  6. 6.
    Csiszár, I. and Narayan, P., The Capacity of the Arbitrarily Varying Channel Revisited: Positivity, Constraints, IEEE Trans. Inform. Theory, 1988, vol. 34, no. 2, pp. 181–193.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ahlswede, R., Elimination of Correlation in Random Codes for Arbitrarily Varying Channels, Z. Wahrsch. Verw. Gebiete, 1978, vol. 44, no. 2, pp. 159–175.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ahlswede, R. and Cai, N., Correlated Sources Help Transmission over an Arbitrarily Varying Channel, IEEE Trans. Inform. Theory, 1997, vol. 43, no. 4, pp. 1254–1255.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Schaefer, R.F. and Boche, H., How Much Coordination Is Needed for Robust Broadcasting over Arbitrarily Varying Bidirectional Broadcast Channels, in Proc. 2014 IEEE Int. Conf. on Communications (ICC’2014), Sydney, Australia, June 10–14, 2014, pp. 1872–1877.Google Scholar
  10. 10.
    Boche, H. and Schaefer, R.F., Capacity Results, Coordination Resources, and Super-activation in Wiretap Channels, in Proc. 2013 IEEE Int. Sympos. on Information Theory (ISIT’2013), Istanbul, Turkey, July 7–12, 2013, pp. 1342–1346.Google Scholar
  11. 11.
    Smith, G. and Yard, J., Quantum Communication with Zero-Capacity Channels, Science, 2008, vol. 321, no. 5897, pp. 1812–1815.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Boche, H., Schaefer, R.F., and Poor, H.V., On Arbitrarily Varying Wiretap Channels for Different Classes of Secrecy Measures, in Proc. 2014 IEEE Int. Sympos. on Information Theory (ISIT’2014), Honolulu, HI, USA, June 29–July 4, 2014, pp. 2376–2380.Google Scholar
  13. 13.
    Nötzel, J., Wiese, M., and Boche, H., The Arbitrarily Varying Wiretap Channel—Secret Randomness, Stability, and Super-activation, IEEE Trans. Inform. Theory, 2016, vol. 62, no. 6, pp. 3504–3531.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Schaefer, R.F., Boche, H., and Poor, H.V., Super-activation as a Unique Feature of Arbitrarily Varying Wiretap Channels, in Proc. 2016 IEEE Int. Sympos. on Information Theory (ISIT’2016), Barcelona, Spain, July 10–15, 2016, pp. 3077–3081.Google Scholar
  15. 15.
    Ahlswede, R., A Note on the Existence of the Weak Capacity for Channels with Arbitrarily Varying Channel Probability Functions and Its Relation to Shannon’s Zero Error Capacity, Ann. Math. Statist., 1970, vol. 41, no. 3, pp. 1027–1033.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Shannon, C.E., The Zero Error Capacity of a Noisy Channel, IRE Trans. Inform. Theory, 1956, vol. 2, no. 3, pp. 8–19.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Alon, N., The Shannon Capacity of a Union, Combinatorica, 1998, vol. 18, no. 3, pp. 301–310.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Ericson, T., Exponential Error Bounds for Random Codes in the Arbitrarily Varying Channel, IEEE Trans. Inform. Theory, 1985, vol. 31, no. 1, pp. 42–48.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Leung, D. and Smith, G., Continuity of Quantum Channel Capacities, Comm. Math. Phys., 2009, vol. 292, no. 1, pp. 201–215.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Boche, H. and Nöotzel, J., Positivity, Discontinuity, Finite Resources, Nonzero Error for Arbitrarily Varying Quantum Channels, in Proc. 2014 IEEE Int. Sympos. on Information Theory (ISIT’2014), Honolulu, HI, USA, June 29–July 4, 2014, pp. 541–545.Google Scholar
  21. 21.
    Boche, H., Schaefer, R.F., and Poor, H.V., On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels, IEEE Trans. Inf. Forensics Secur., 2015, vol. 10, no. 12, pp. 2531–2546.CrossRefGoogle Scholar
  22. 22.
    Arendt, C., Nöotzel, J., and Boche, H., Super-activation of the Composite Independent Arbitrarily Varying Channel under State Constraints, in Proc. IEEE Global Communications Conf. (GLOBECOM’2017), Singapore, Dec. 4–8, 2017, pp. 1–6.Google Scholar
  23. 23.
    Nötzel, J. and Swetly, W., Deducing Truth from Correlation, IEEE Trans. Inform. Theory, 2016, vol. 62, no. 12, pp. 7505–7517.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Noötzel, J. and Arendt, C., Using Dependent Component Analysis for Blind Channel Estimation in Distributed Antenna Systems, in Proc. 2016 Global Conf. on Signal and Information Processing (GlobalSIP’2016), Washington, DC, USA, Dec. 7–9, 2016, pp. 1116–1121.Google Scholar
  25. 25.
    Ahlswede, R. and Cai, N., Arbitrarily Varying Multiple-Access Channels. II: Correlated Sender’s Side Information, Correlated Messages, and Ambiguous Transmission, in Proc. 1997 IEEE Int. Sympos. on Information Theory (ISIT’97), Ulm, Germany, June 29–July 4, 1997, p. 23.Google Scholar
  26. 26.
    Boche, H. and Nöotzel, J., Positivity, Discontinuity, Finite Resources, and Nonzero Error for Arbitrarily Varying Quantum Channels, J. Math. Phys., 2014, vol. 55, no. 12, p. 122201 (20 pp.).MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Stiglitz, I.G., Coding for a Class of Unknown Channels, IEEE Trans. Inform. Theory, 1966, vol. 12, no. 2, pp. 189–195.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    IEEE 802.11-2016: IEEE Standard for Information Technology—Telecommunications and Information Exchange between Systems. Local and Metropolitan Area Networks—Specific Requirements. Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. 2016.Google Scholar
  29. 29.
    ETSI ES 202 663 V1.1.0 (2009-11): ETSI Standard Intelligent Transport Systems (ITS); European Profile Standard for the Physical and Medium Access Control Layer of Intelligent Transport Systems Operating in the 5 GHz Frequency Band. Final draft, 2011.Google Scholar
  30. 30.
    Uhlemann, E., Initial Steps toward a Cellular Vehicle-to-Everything Standard [Connected Vehicles], IEEE Veh. Technol. Mag., 2017, vol. 12, no. 1, pp. 14–19.CrossRefGoogle Scholar
  31. 31.
    Khan, A., Almeida, J., Fernandes, B., Alam, M., Pedreiras, P., and Ferreira, J., Towards Reliable Wireless Vehicular Communications, in Proc. 2015 IEEE 18th Int. Conf. on Intelligent Transportation Systems (ITSC’2015), Canary Islands, Spain, Sept. 15–18, 2015, pp. 167–172.Google Scholar
  32. 32.
    Arendt, C., Nöotzel, J., and Boche, H., Evaluation of Distributed Post-Detection Receive Diversity Combining Schemes for Reliable Wireless Communication over Arbitrarily Varying Channels, in Proc. 2018 IEEE 88th Vehicular Technology Conf. (VTC-Fall), Chicago, IL, USA, Aug. 27–30, 2018, pp. 1–6.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.BMW GroupMünchenGermany
  2. 2.Lehrstuhl für Theoretische InformationstechnikTechnische Universität MünchenMünchenGermany

Personalised recommendations