Document Open Access Logo

Interactive Coding with Unbounded Noise

Authors Eden Fargion , Ran Gelles , Meghal Gupta

PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2024.43.pdf
  • Filesize: 0.72 MB
  • 16 pages

Document Identifiers

Author Details

Eden Fargion
  • Faculty of Engineering, Bar-Ilan University, Ramat-Gan, Israel
Ran Gelles
  • Faculty of Engineering, Bar-Ilan University, Ramat-Gan, Israel
Meghal Gupta
  • University of California, Berkeley, CA, USA

Funding

  • Gelles, Ran: partially supported by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, Grant No. 2020277.

Acknowledgements

E. Fargion and R. Gelles would like to thank Paderborn University for hosting them while part of this research was done. R. Gelles would like to thank CISPA - Helmholtz Center for Information Security for hosting him.

Cite AsGet BibTex

Eden Fargion, Ran Gelles, and Meghal Gupta. Interactive Coding with Unbounded Noise. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.43

Abstract

Interactive coding allows two parties to conduct a distributed computation despite noise corrupting a certain fraction of their communication. Dani et al. (Inf. and Comp., 2018) suggested a novel setting in which the amount of noise is unbounded and can significantly exceed the length of the (noise-free) computation. While no solution is possible in the worst case, under the restriction of oblivious noise, Dani et al. designed a coding scheme that succeeds with a polynomially small failure probability. We revisit the question of conducting computations under this harsh type of noise and devise a computationally-efficient coding scheme that guarantees the success of the computation, except with an exponentially small probability. This higher degree of correctness matches the case of coding schemes with a bounded fraction of noise. Our simulation of an N-bit noise-free computation in the presence of T corruptions, communicates an optimal number of O(N+T) bits and succeeds with probability 1-2^(-Ω(N)). We design this coding scheme by introducing an intermediary noise model, where an oblivious adversary can choose the locations of corruptions in a worst-case manner, but the effect of each corruption is random: the noise either flips the transmission with some probability or otherwise erases it. This randomized abstraction turns out to be instrumental in achieving an optimal coding scheme.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive computation
  • Mathematics of computing → Coding theory
  • Computing methodologies → Distributed algorithms
Keywords
  • Distributed Computation with Noisy Links
  • Interactive Coding
  • Noise Resilience
  • Unbounded Noise
  • Random Erasure-Flip Noise

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Abhinav Aggarwal, Varsha Dani, Thomas P. Hayes, and Jared Saia. A scalable algorithm for multiparty interactive communication with private channels. In ICDCN 2020: 21st International Conference on Distributed Computing and Networking, Kolkata, India, January 4-7, 2020, ICDCN '20, pages 8:1-8:15, New York, NY, USA, 2020. Association for Computing Machinery. URL: https://doi.org/10.1145/3369740.3369771.
  2. Zvika Brakerski, Yael T. Kalai, and Moni Naor. Fast interactive coding against adversarial noise. J. ACM, 61(6):35:1-35:30, December 2014. URL: https://doi.org/10.1145/2661628.
  3. Mark. Braverman and Klim. Efremenko. List and unique coding for interactive communication in the presence of adversarial noise. SIAM Journal on Computing, 46(1):388-428, 2017. URL: https://doi.org/10.1137/141002001.
  4. Mark Braverman, Ran Gelles, Jieming Mao, and Rafail Ostrovsky. Coding for interactive communication correcting insertions and deletions. IEEE Transactions on Information Theory, 63(10):6256-6270, October 2017. URL: https://doi.org/10.1109/TIT.2017.2734881.
  5. Mark Braverman and Anup Rao. Toward coding for maximum errors in interactive communication. IEEE Transactions on Information Theory, 60(11):7248-7255, November 2014. URL: https://doi.org/10.1109/TIT.2014.2353994.
  6. Ronald Cramer, Yevgeniy Dodis, Serge Fehr, Carles Padró, and Daniel Wichs. Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors. In Nigel P. Smart, editor, Advances in Cryptology - EUROCRYPT 2008, 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Istanbul, Turkey, April 13-17, 2008. Proceedings, volume 4965, pages 471-488, Berlin, Heidelberg, 2008. Springer. URL: https://doi.org/10.1007/978-3-540-78967-3_27.
  7. Varsha Dani, Thomas P. Hayes, Mahnush Movahedi, Jared Saia, and Maxwell Young. Interactive communication with unknown noise rate. Information and Computation, 261:464-486, 2018. URL: https://doi.org/10.1016/j.ic.2018.02.018.
  8. Klim Efremenko, Ran Gelles, and Bernhard Haeupler. Maximal noise in interactive communication over erasure channels and channels with feedback. IEEE Transactions on Information Theory, 62(8):4575-4588, August 2016. URL: https://doi.org/10.1109/TIT.2016.2582176.
  9. Klim Efremenko, Elad Haramaty, and Yael Tauman Kalai. Interactive coding with constant round and communication blowup. In Thomas Vidick, editor, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, January 12-14, 2020, Seattle, Washington, USA, volume 151 of Leibniz International Proceedings in Informatics (LIPIcs), pages 7:1-7:34, Dagstuhl, Germany, 2020. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.7.
  10. Eden Fargion, Ran Gelles, and Meghal Gupta. Interactive coding with unbounded noise, 2024. URL: https://arxiv.org/abs/2407.09463.
  11. Matthew Franklin, Ran Gelles, Rafail Ostrovsky, and Leonard J. Schulman. Optimal coding for streaming authentication and interactive communication. IEEE Transactions on Information Theory, 61(1):133-145, January 2015. URL: https://doi.org/10.1109/TIT.2014.2367094.
  12. Ran Gelles. Coding for interactive communication: A survey. Foundations and Trends® in Theoretical Computer Science, 13(1-2):1-157, 2017. URL: https://doi.org/10.1561/0400000079.
  13. Ran Gelles and Bernhard Haeupler. Capacity of interactive communication over erasure channels and channels with feedback. SIAM Journal on Computing, 46(4):1449-1472, 2017. URL: https://doi.org/10.1137/15M1052202.
  14. Ran Gelles, Bernhard Haeupler, Gillat Kol, Noga Ron-Zewi, and Avi Wigderson. Explicit capacity approaching coding for interactive communication. IEEE Transactions on Information Theory, 64(10):6546-6560, October 2018. URL: https://doi.org/10.1109/TIT.2018.2829764.
  15. Ran Gelles and Siddharth Iyer. Interactive coding resilient to an unknown number of erasures. In 23rd International Conference on Principles of Distributed Systems, OPODIS 2019, December 17-19, 2019, Neuchâtel, Switzerland, volume 153 of Leibniz International Proceedings in Informatics (LIPIcs), pages 13:1-13:16, 2019. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2019.13.
  16. 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. URL: https://doi.org/10.1109/TIT.2021.3066009.
  17. 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. URL: https://doi.org/10.1109/TIT.2022.3160515.
  18. Ran Gelles, Ankur Moitra, and Amit Sahai. Efficient coding for interactive communication. IEEE Transactions on Information Theory, 60(3):1899-1913, March 2014. URL: https://doi.org/10.1109/TIT.2013.2294186.
  19. Mohsen Ghaffari and Bernhard Haeupler. Optimal error rates for interactive coding II: efficiency and list decoding. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18-21, 2014, pages 394-403. IEEE Computer Society, 2014. URL: https://doi.org/10.1109/FOCS.2014.49.
  20. Meghal Gupta and Rachel Yun Zhang. The optimal error resilience of interactive communication over binary channels. In STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, STOC 2022, pages 948-961, 2022. URL: https://doi.org/10.1145/3519935.3519985.
  21. Bernhard Haeupler. Interactive channel capacity revisited. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18-21, 2014, pages 226-235, 2014. URL: https://doi.org/10.1109/FOCS.2014.32.
  22. Bernhard Haeupler, Amirbehshad Shahrasbi, and Ellen Vitercik. Synchronization strings: Channel simulations and interactive coding for insertions and deletions. In 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, volume 107 of Leibniz International Proceedings in Informatics (LIPIcs), pages 75:1-75:14, 2018. URL: https://doi.org/10.4230/LIPIcs.ICALP.2018.75.
  23. Gillat Kol and Ran Raz. Interactive channel capacity. In Symposium on Theory of Computing Conference, STOC'13, Palo Alto, CA, USA, June 1-4, 2013, pages 715-724, 2013. URL: https://doi.org/10.1145/2488608.2488699.
  24. Michael Mitzenmacher and Eli Upfal. Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis. Cambridge University Press, USA, 2nd edition, 2017. Google Scholar
  25. Leonard J. Schulman. Communication on noisy channels: A coding theorem for computation. In 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, Pennsylvania, USA, 24-27 October 1992, pages 724-733, Los Alamitos, CA, USA, 1992. IEEE Computer Society. URL: https://doi.org/10.1109/SFCS.1992.267778.
  26. Leonard J. Schulman. Coding for interactive communication. IEEE Transactions on Information Theory, 42(6):1745-1756, November 1996. URL: https://doi.org/10.1109/18.556671.
  27. Alexander A. Sherstov and Pei Wu. Optimal interactive coding for insertions, deletions, and substitutions. IEEE Transactions on Information Theory, 65(10):5971-6000, October 2019. URL: https://doi.org/10.1109/TIT.2019.2916927.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact