Interactive Coding with Unbounded Noise

Eden Fargion, Ran Gelles, Meghal Gupta

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 − 2Ω(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.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024
EditorsAmit Kumar, Noga Ron-Zewi
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773485
DOIs
StatePublished - Sep 2024
Event27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024 - London, United Kingdom
Duration: 28 Aug 202430 Aug 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume317
ISSN (Print)1868-8969

Conference

Conference27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024
Country/TerritoryUnited Kingdom
CityLondon
Period28/08/2430/08/24

Bibliographical note

Publisher Copyright:
© Eden Fargion, Ran Gelles, and Meghal Gupta.

Keywords

  • Distributed Computation with Noisy Links
  • Interactive Coding
  • Noise Resilience
  • Random Erasure-Flip Noise
  • Unbounded Noise

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