Interactive Coding with Unbounded Noise

TL;DR

This paper presents a new efficient interactive coding scheme that reliably computes in the presence of unbounded, oblivious noise, achieving near-perfect success probability with optimal communication complexity.

Contribution

It introduces a computationally-efficient coding scheme for unbounded noise with exponentially small failure probability, improving upon prior polynomially small failure guarantees.

Findings

Achieves success probability of 1-2^{- ext{Omega}(N)}

Communicates an optimal O(N+T) bits in the presence of T corruptions

Introduces a randomized noise model to facilitate coding scheme design

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 $1-2^{-\Omega(N)}$. 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.