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.

翻译：交互式编码使得两方能够在通信中部分信息被噪声干扰的情况下进行分布式计算。Dani等人（Inf. and Comp., 2018）提出了一种新颖的场景，其中噪声量是无界的，可能显著超过（无噪声）计算的长度。虽然在最坏情况下无法找到解决方案，但在无记忆噪声的限制下，Dani等人设计了一种编码方案，其失败概率为多项式小。我们重新审视了在这种严苛噪声类型下进行计算的问题，并设计了一种计算高效的编码方案，该方案保证计算成功，除非出现指数级小的概率。这种更高的正确性程度与具有有界噪声比例的编码方案情况相匹配。我们在存在$T$次干扰的情况下模拟$N$比特无噪声计算，以最优的$O(N+T)$比特通信量进行，并以$1-2^{-\Omega(N)}$的概率成功。我们通过引入一种中间噪声模型来设计此编码方案，其中无记忆的对手可以以最坏情况的方式选择干扰位置，但每次干扰的效果是随机的：噪声要么以一定概率翻转传输，要么将其擦除。事实证明，这种随机化抽象对于实现最优编码方案至关重要。