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Information Dissemination via Broadcasts in the Presence of Adversarial Noise

Authors Klim Efremenko , Gillat Kol , Dmitry Paramonov , Ran Raz , Raghuvansh R. Saxena

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Author Details

Klim Efremenko
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Gillat Kol
  • Princeton University, NJ, USA
Dmitry Paramonov
  • Princeton University, NJ, USA
Ran Raz
  • Princeton University, NJ, USA
Raghuvansh R. Saxena
  • Tata Institute of Fundamental Research, Mumbai, India

Funding

  • Efremenko, Klim: Supported by European Research Council Grant No. 949707.
  • Kol, Gillat: Supported by the National Science Foundation CAREER award CCF-1750443.
  • Raz, Ran: Supported by a Simons Investigator Award and by the National Science Foundation grant No. CCF-2007462.

Cite AsGet BibTex

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena. Information Dissemination via Broadcasts in the Presence of Adversarial Noise. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 19:1-19:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CCC.2024.19

Abstract

We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where n parties, each holding an input bit, wish to know each other’s input. For this, they communicate in rounds, where, in each round, one designated party sends a bit to all other parties over a channel governed by an adversary that may corrupt a constant fraction of the received communication. We mention that the dissemination problem was studied in the stochastic noise model since the 80’s. While stochastic noise in multi-party channels has received quite a bit of attention, the case of adversarial noise has largely been avoided, as such channels cannot handle more than a 1/n-fraction of errors. Indeed, this many errors allow an adversary to completely corrupt the incoming or outgoing communication for one of the parties and fail the protocol. Curiously, we show that by eliminating these "trivial" attacks, one can get a simple protocol resilient to a constant fraction of errors. Thus, a model that rules out such attacks is both necessary and sufficient to get a resilient protocol. The main shortcoming of our dissemination protocol is its length: it requires Θ(n²) communication rounds whereas n rounds suffice in the absence of noise. Our main result is a matching lower bound of Ω(n²) on the length of any dissemination protocol in our model. Our proof first "gets rid" of the channel noise by converting it to a form of "input noise", showing that a noisy dissemination protocol implies a (noiseless) protocol for a version of the direct sum gap-majority problem. We conclude the proof with a tight lower bound for the latter problem, which may be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
Keywords
  • Radio Networks
  • Interactive Coding
  • Error Correcting Codes

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References

  1. Abhinav Aggarwal, Varsha Dani, Thomas P Hayes, and Jared Saia. Distributed computing with channel noise. arXiv preprint, 2016. URL: https://arxiv.org/abs/1612.05943.
  2. Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, and Bernhard Haeupler. Reliable communication over highly connected noisy networks. In Symposium on Principles of Distributed Computing (DISC), pages 165-173. ACM, 2016. Google Scholar
  3. Ziv Bar-Yossef, Thathachar S Jayram, Ravi Kumar, and D Sivakumar. An information statistics approach to data stream and communication complexity. Journal of Computer and System Sciences, 68(4):702-732, 2004. Google Scholar
  4. Boaz Barak, Mark Braverman, Xi Chen, and Anup Rao. How to compress interactive communication. SIAM Journal on Computing, 42(3):1327-1363, 2013. Google Scholar
  5. Mark Braverman, Klim Efremenko, Ran Gelles, and Bernhard Haeupler. Constant-rate coding for multiparty interactive communication is impossible. In Symposium on Theory of Computing (STOC), pages 999-1010. ACM, 2016. Google Scholar
  6. Mark Braverman and Anup Rao. Information equals amortized communication. In Rafail Ostrovsky, editor, Symposium on Foundations of Computer Science (FOCS), pages 748-757. IEEE Computer Society, 2011. Google Scholar
  7. Mark Braverman, Anup Rao, Omri Weinstein, and Amir Yehudayoff. Direct product via round-preserving compression. In International Colloquium on Automata, Languages, and Programming (ICALP), pages 232-243. Springer, 2013. Google Scholar
  8. Mark Braverman, Anup Rao, Omri Weinstein, and Amir Yehudayoff. Direct products in communication complexity. In Symposium on Foundations of Computer Science (FOCS), pages 746-755. IEEE, 2013. Google Scholar
  9. Keren Censor-Hillel, Ran Gelles, and Bernhard Haeupler. Making asynchronous distributed computations robust to noise. Distributed Computing, 32:405-421, 2019. Google Scholar
  10. Keren Censor-Hillel, Bernhard Haeupler, D Ellis Hershkowitz, and Goran Zuzic. Broadcasting in noisy radio networks. In Symposium on Principles of Distributed Computing (PODC), pages 33-42, 2017. Google Scholar
  11. Keren Censor-Hillel, Bernhard Haeupler, D Ellis Hershkowitz, and Goran Zuzic. Erasure correction for noisy radio networks. In International Symposium on Distributed Computing (DISC), 2019. Google Scholar
  12. Amit Chakrabarti, Yaoyun Shi, Anthony Wirth, and Andrew Yao. Informational complexity and the direct sum problem for simultaneous message complexity. In Symposium on Foundations of Computer Science (FOCS), pages 270-278. IEEE, 2001. Google Scholar
  13. Imrich Chlamtac and Shay Kutten. On broadcasting in radio networks-problem analysis and protocol design. IEEE Trans. Communications, 33(12):1240-1246, 1985. Google Scholar
  14. Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Computation over the noisy broadcast channel with malicious parties. In Innovations in Theoretical Computer Science Conference, (ITCS), volume 185, pages 82:1-82:19, 2021. Google Scholar
  15. Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Tight bounds for general computation in noisy broadcast networks. In Symposium on Foundations of Computer Science (FOCS), pages 634-645, 2021. Google Scholar
  16. Klim Efremenko, Gillat Kol, Dmitry Paramonov, and Raghuvansh R. Saxena. Protecting single-hop radio networks from message drops. In Kousha Etessami, Uriel Feige, and Gabriele Puppis, editors, International Colloquium on Automata, Languages, and Programming (ICALP), volume 261 of LIPIcs, pages 53:1-53:20, 2023. Google Scholar
  17. Klim Efremenko, Gillat Kol, and Raghuvansh Saxena. Interactive coding over the noisy broadcast channel. In Symposium on Theory of Computing (STOC), pages 507-520. ACM, 2018. Google Scholar
  18. Klim Efremenko, Gillat Kol, and Raghuvansh Saxena. Radio network coding requires logarithmic overhead. In Foundations of Computer Science (FOCS), pages 348-369, 2019. Google Scholar
  19. Klim Efremenko, Gillat Kol, and Raghuvansh Saxena. Interactive error resilience beyond 2/7. In Symposium on Theory of Computing (STOC). ACM, 2020. Google Scholar
  20. Klim Efremenko, Gillat Kol, and Raghuvansh R. Saxena. Noisy beeps. In Yuval Emek and Christian Cachin, editors, Symposium on Principles of Distributed Computing (PODC), pages 418-427, 2020. Google Scholar
  21. Klim Efremenko, Gillat Kol, and Raghuvansh R. Saxena. Optimal error resilience of adaptive message exchange. In Symposium on Theory of Computing (STOC), pages 1235-1247. ACM, 2021. Google Scholar
  22. Tomás Feder, Eyal Kushilevitz, Moni Naor, and Noam Nisan. Amortized communication complexity. SIAM Journal on computing, 24(4):736-750, 1995. Google Scholar
  23. Uriel Feige and Joe Kilian. Finding OR in a noisy broadcast network. Information Processing Letters, 73(1-2):69-75, 2000. Google Scholar
  24. Robert G. Gallager. Finding parity in a simple broadcast network. IEEE Transactions on Information Theory, 34(2):176-180, 1988. Google Scholar
  25. Abbas El Gamal. Open problems presented at the 1984 workshop on specific problems in communication and computation sponsored by bell communication research. "Open Problems in Communication and Computation", by Thomas M. Cover and B. Gopinath (editors). Springer-Verlag, 1987. Google Scholar
  26. Anat Ganor, Gillat Kol, and Ran Raz. Exponential separation of information and communication for boolean functions. Journal of the ACM, 63(5):46:1-46:31, 2016. Google Scholar
  27. Anat Ganor, Gillat Kol, and Ran Raz. Exponential separation of communication and external information. SIAM Journal on computing, 50(3), 2021. Google Scholar
  28. Ran Gelles and Yael T Kalai. Constant-rate interactive coding is impossible, even in constant-degree networks. IEEE Transactions on Information Theory, 65(6):3812-3829, 2019. Google Scholar
  29. Ran Gelles, Yael Tauman Kalai, and Govind Ramnarayan. Efficient multiparty interactive coding—part i: Oblivious insertions, deletions and substitutions. IEEE Transactions on Information Theory, 67(6):3411-3437, 2021. Google Scholar
  30. Ran Gelles, Yael Tauman Kalai, and Govind Ramnarayan. Efficient multiparty interactive coding—part ii: Non-oblivious noise. IEEE Transactions on Information Theory, 68(7):4723-4749, 2022. Google Scholar
  31. Ran Gelles, Ankur Moitra, and Amit Sahai. Efficient and explicit coding for interactive communication. In 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pages 768-777. IEEE, 2011. Google Scholar
  32. Navin Goyal, Guy Kindler, and Michael Saks. Lower bounds for the noisy broadcast problem. SIAM Journal on Computing, 37(6):1806-1841, 2008. Google Scholar
  33. Bernhard Haeupler. Interactive channel capacity revisited. In Foundations of Computer Science (FOCS), pages 226-235. IEEE, 2014. Google Scholar
  34. Prahladh Harsha, Rahul Jain, David McAllester, and Jaikumar Radhakrishnan. The communication complexity of correlation. In Conference on Computational Complexity (CCC), pages 10-23. IEEE, 2007. Google Scholar
  35. William M. Hoza and Leonard J. Schulman. The adversarial noise threshold for distributed protocols. In Symposium on Discrete Algorithms (SODA), pages 240-258, 2016. Google Scholar
  36. Abhishek Jain, Yael Tauman Kalai, and Allison Bishop Lewko. Interactive coding for multiparty protocols. In Symposium on Theory of computing (STOC), pages 1-10, 2015. Google Scholar
  37. Rahul Jain. New strong direct product results in communication complexity. Journal of the ACM, 62(3):1-27, 2015. Google Scholar
  38. Rahul Jain, Attila Pereszlényi, and Penghui Yao. A direct product theorem for two-party bounded-round public-coin communication complexity. Algorithmica, 76:720-748, 2016. Google Scholar
  39. Rahul Jain, Jaikumar Radhakrishnan, and Pranab Sen. A direct sum theorem in communication complexity via message compression. In Colloquium on Automata, Languages, and Programming (ICALP), pages 300-315. Springer, 2003. Google Scholar
  40. Mauricio Karchmer, Eyal Kushilevitz, and Noam Nisan. Fractional covers and communication complexity. SIAM Journal on Discrete Mathematics, 8(1):76-92, 1995. Google Scholar
  41. Hartmut Klauck. A strong direct product theorem for disjointness. In Symposium on Theory of Computing (STOC), pages 77-86, 2010. Google Scholar
  42. Eyal Kushilevitz and Yishay Mansour. Computation in noisy radio networks. SIAM Journal on Discrete Mathematics (SIDMA), 19(1):96-108, 2005. Google Scholar
  43. Allison Lewko and Ellen Vitercik. Balancing communication for multi-party interactive coding. arXiv preprint, 2015. URL: https://arxiv.org/abs/1503.06381.
  44. Manuj Mukherjee and Ran Gelles. Multiparty interactive coding over networks of intersecting broadcast links. IEEE Journal on Selected Areas in Information Theory, 2(4):1078-1092, 2021. Google Scholar
  45. Ilan Newman. Computing in fault tolerance broadcast networks. In Computational Complexity Conference (CCC), pages 113-122, 2004. Google Scholar
  46. Sridhar Rajagopalan and Leonard J. Schulman. A coding theorem for distributed computation. In Symposium on the Theory of Computing (STOC), pages 790-799, 1994. Google Scholar
  47. Leonard J Schulman. Communication on noisy channels: A coding theorem for computation. In Foundations of Computer Science (FOCS), pages 724-733. IEEE, 1992. Google Scholar
  48. Andrew Chi-Chih Yao. On the complexity of communication under noise. invited talk in the 5th ISTCS Conference, 1997. Google Scholar
  49. Huacheng Yu. Strong xor lemma for communication with bounded rounds. In Symposium on Foundations of Computer Science (FOCS), pages 1186-1192. IEEE, 2022. Google Scholar
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