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Interactive Coding with Unbounded Noise

Authors Eden Fargion , Ran Gelles , Meghal Gupta

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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 As Get 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

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References

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