Interactive Coding with Unbounded Noise
<|reference_start|>Interactive Coding with Unbounded Noise: 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 $1-2^{-\Omega(N)}$. 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.<|reference_end|>
@article{fargion2024interactive,
    title={Interactive Coding with Unbounded Noise},
    author={Eden Fargion, Ran Gelles and Meghal Gupta},
    journal={arXiv preprint arXiv:2407.09463},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09463},
    primaryClass={cs.DS}
}