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.
Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024 |
Editors | Amit Kumar, Noga Ron-Zewi |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959773485 |
DOIs | |
State | Published - Sep 2024 |
Event | 27th 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 2024 → 30 Aug 2024 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 317 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024 |
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Country/Territory | United Kingdom |
City | London |
Period | 28/08/24 → 30/08/24 |
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