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Clock Synchronization and Estimation in Highly Dynamic Networks: An Information Theoretic Approach

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Structural Information and Communication Complexity (SIROCCO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9439))

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Abstract

We consider the External Clock Synchronization problem in dynamic sensor networks. Initially, sensors obtain inaccurate estimations of an external time reference and subsequently collaborate in order to synchronize their internal clocks with the external time. For simplicity, we adopt the drift-free assumption, where internal clocks are assumed to tick at the same pace. Hence, the problem is reduced to an estimation problem, in which the sensors need to estimate the initial external time. In this context of distributed estimation, this work is further relevant to the problem of collective approximation of environmental values by biological groups.

Unlike most works on clock synchronization that assume static networks, this paper focuses on an extreme case of highly dynamic networks. We do however impose a restriction on the dynamicity of the network. Specifically, we assume a non-adaptive scheduler adversary that dictates an arbitrary, yet independent, meeting pattern. Such meeting patterns fit, for example, with short-time scenarios in highly dynamic settings, where each sensor interacts with only few other arbitrary sensors.

We propose an extremely simple clock synchronization (or an estimation) algorithm that is based on weighted averages, and prove that its performance on any given independent meeting pattern is highly competitive with that of the best possible algorithm, which operates without any resource or computational restrictions, and further knows the whole meeting pattern in advance. In particular, when all distributions involved are Gaussian, the performances of our scheme coincide with the optimal performances. Our proofs rely on an extensive use of the concept of Fisher information. We use the Cramér-Rao bound and our definition of a Fisher Channel Capacity to quantify information flows and to obtain lower bounds on collective performance. This opens the door for further rigorous quantifications of information flows within collaborative sensors.

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References

  1. Angluin, D.: Local and global properties in networks of processors. In: STOC, pp. 82–93 (1980)

    Google Scholar 

  2. Attiya, H., Herzberg, A., Rajsbaum, S.: Optimal Clock Synchronization under Different Delay Assumptions. SIAM J. Comput. 25(2), 369–389 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bar-Yossef, Z., Jayram, T.S., Kumar, R., Sivakumar, D.: Info. Theory Methods in Comm. Complexity. IEEE Conf. on Computational Complexity, 93–102 (2002)

    Google Scholar 

  4. Biaz, S., Welch, J.L.: Closed form bounds for clock synchronization under simple uncertainty assumptions. Inf. Process. Lett. 80(3), 151–157 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Blachman, N.M.: The convolution inequality for entropy powers. IEEE Transactions on Information Theory 11(2), 267–271 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chaudhari, Q., Serpedin, E., Wu, Y.C.: Improved estimation of clock offset in sensor networks. In: ICC (2009)

    Google Scholar 

  7. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. John Wiley & Sons (2006)

    Google Scholar 

  8. Cristian, F.: Probabilistic Clock Synchronization. Distributed Computing 3(3), 146–158 (1989)

    Article  MATH  Google Scholar 

  9. Dolev, D., Halpern, J., Simons, B., Strong, R.: Dynamic fault-tolerant clock synchronization. Journal of the ACM 42(1), 143–185 (1995)

    Article  MATH  Google Scholar 

  10. Elson, J., Girod, L., Estrin, D.: Fine-Grained Network Time Synchronization Using Reference Broadcasts. Operating Systems Review 36, 147–163 (2002)

    Article  Google Scholar 

  11. Feinerman, O., Haeupler, B., Korman, A.: Breathe before speaking: efficient information dissemination despite noisy, limited and anonymous communication. In: PODC, pp. 114–123 (2014)

    Google Scholar 

  12. Feinerman, O., Korman, A.: Clock Synchronization and Estimation in Highly Dynamic Networks: An Information Theoretic Approach (An Arxiv version). http://arxiv.org/pdf/1504.08247v1.pdf

  13. El Gamal, A., Kim, Y.: Network Information Theory, 709 p. Cambridge University Press (2012)

    Google Scholar 

  14. Gubner, J.: Distributed Estimation and Quantization. IEEE Tran. on Information Theory 39(4) (1993)

    Google Scholar 

  15. Jeske, D.: On the maximum likelihood estimation of clock offset. IEEE Trans. Commun. 53(1) (2005)

    Google Scholar 

  16. Kar, S., Moura, J.M.F.: Distributed Consensus Algorithms in Sensor Networks With Imperfect Communication: Link Failures and Channel Noise. IEEE Tran. on SIgnal Processing 57(1), 355–369 (2009)

    Article  MathSciNet  Google Scholar 

  17. Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: FOCS 2003, pp. 482–449 (2003)

    Google Scholar 

  18. Koetter, R., Kschischang, F.R.: Coding for errors and erasures in random network coding. IEEE Transactions on Info. Theory 54(8), 3579–3591 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Korman, A., Greenwald, E., Feinerman, O.: Confidence Sharing: an Economic Strategy for Efficient Information Flows in Animal Groups. PLOS Computational Biology 10(10) (2014)

    Google Scholar 

  20. Kuhn, F., Lenzen, C., Locher, T., Oshman, R.: Optimal gradient clock synchronization in dynamic networks. In: PODC, pp. 430–439 (2010)

    Google Scholar 

  21. Lamport, L.: Proving the Correctness of Multiprocess Programs. IEEE Transactions on Software Engineering (2), 125–143 (1977)

    Google Scholar 

  22. Lenzen, C., Locher, T., Wattenhofer, R.: Tight Bounds for Clock Synchronization. JACM 57(2) (2010)

    Google Scholar 

  23. Lenzen, C., Sommer, P., Wattenhofer, R.: PulseSync: An Efficient and Scalable Clock Synchronization Protocol. ACM/IEEE Transactions on Networking (2014)

    Google Scholar 

  24. Lenzen, C., Locher, T., Sommer, P., Wattenhofer, R.: Clock synchronization: Open problems in theory and practice. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 61–70. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  25. Lundelius, J., Lynch, N.: An Upper and Lower Bound for Clock Synchronization. Information and Control 62, 190–204 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  26. McNamara, J.M., Houston, A.I.: Memory and the efficient use of information. Journal of Theoretical Biology 125(4), 385–395 (1987)

    Article  MathSciNet  Google Scholar 

  27. Mills, D.L.: Internet time synchronization: the network time protocol. IEEE Transactions of Communications 39(10), 1482–1493 (1991)

    Article  Google Scholar 

  28. Mills, D.L.: Improved algorithms for synchronizing computer network clocks. Networks 3, 3 (1995)

    Google Scholar 

  29. Ostrovsky, R., Patt-Shamir, B.: Optimal and efficient clock synchronization under drifting clocks. In: PODC 1999, pp. 3–12 (1999)

    Google Scholar 

  30. Patt-Shamir, B., Rajsbaum, S.: A theory of clock synchronization. In: STOC 1994, pp. 810–819 (1994)

    Google Scholar 

  31. Rioul, O.: Information theoretic proofs of entropy power inequalities. IEEE Transactions on Information Theory 57(1), 33–55 (2011)

    Article  MathSciNet  Google Scholar 

  32. Sivrikaya, F., Yener, B.: Time synchronization in sensor networks: a survey. IEEE Network 18(4) (2004)

    Google Scholar 

  33. Shannon, C.: A Mathematical Theory of Communication. Technical Journal 27(3), 379–423 (1948)

    MathSciNet  MATH  Google Scholar 

  34. Solis, R., Borkar, V., Kumar, P.R.: A new distributed time synchronization protocol for multihop wireless networks. In: Proc. 45th IEEE Conference on Decision and Control (CDC) (2006)

    Google Scholar 

  35. Stam, A.J.: Some inequalities satisfied by the quantities of information of Fisher and Shannon. Inform. and Control 2, 101–112 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  36. Xiao, L., Boyd, S., Lall, S.: A scheme for robust distributed sensor fusion based on average consensus. In: Proc. of the 4th International Symposium on Information Processing in Sensor Networks (IPSN) (2005)

    Google Scholar 

  37. Sundararaman, B., Buy, U., Kshemkalyani, A.D.: Clock synchronization for wireless sensor networks: a survey. Ad Hoc Networks 3, 281–323 (2005)

    Article  Google Scholar 

  38. Viswanathan, R., Varshney, P.K.: Distributed detection with multiple sensors I. Fundamentals. Proceedings of the IEEE (1997)

    Google Scholar 

  39. Wu, Y.C., Chaudhari, Q.M., Serpedin, E.: Clock Synchronization of Wireless Sensor Networks. IEEE Signal Process. Mag. 28(1), 124–138 (2011)

    Article  Google Scholar 

  40. Zamir, R.: A proof of the Fisher Information inequality via a data processing arguement. IEEE Trans. Inf. Theory, 482–491 (2003)

    Google Scholar 

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Authors and Affiliations

  1. The Shlomo and Michla Tomarin Career Development Chair, The Weizmann Institute of Science, Rehovot, Israel

    Ofer Feinerman

  2. CNRS and University Paris Diderot, Paris, 75013, France

    Amos Korman

Authors
  1. Ofer Feinerman
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  2. Amos Korman
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Correspondence to Ofer Feinerman .

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Editors and Affiliations

  1. Dept of Mathematics and Comp Science, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Christian Scheideler

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Feinerman, O., Korman, A. (2015). Clock Synchronization and Estimation in Highly Dynamic Networks: An Information Theoretic Approach. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-25258-2_2

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