无界噪声下的交互式编码
Interactive Coding with Unbounded Noise
AI总结：
该研究针对无界健忘噪声场景下的交互式编码问题，引入中间随机噪声模型，设计出计算高效的最优编码方案，实现指数级小的失败概率，性能匹配有界噪声编码水平。
摘要：
交互式编码允许双方在一定比例的通信被噪声破坏的情况下完成分布式计算。Dani等人（《信息与计算》，2018年）提出了一种新的场景，其中噪声量是无界的，可能远超（无噪声的）计算长度。虽然在最坏情况下不存在可行解，但在健忘噪声的限制下，Dani等人设计了一种编码方案，其失败概率仅为多项式级的小概率。\n 我们重新研究了在这种强噪声下进行计算的问题，设计了一种计算高效的编码方案，该方案可保证计算成功，仅存在指数级小的失败概率。这种更高的正确性水平与有界噪声比例下的编码方案性能相当。\n 我们针对N比特无噪声计算在存在T个错误的场景下的仿真，传输了最优的O(N+T)比特，成功概率为1-2^{-Ω(N)}。我们通过引入一种中间噪声模型来设计该编码方案：在该模型中，健忘的敌手可以以最坏情况的方式选择错误发生的位置，但每个错误的影响是随机的——噪声要么以一定概率翻转传输内容，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。
英文摘要：
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.
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