SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, Page 904-937, January 2020.
We consider the task of communicating an (infinite) data stream in the sliding window model, where communication takes place over a noisy channel with an adversarial substitution noise rate up to 1. Specifically, for any noise level ${p<1}$ and any small $\varepsilon>0$, we design an efficient coding scheme, such that as long as the effective noise level in the sliding window is below $p$, the receiver decodes at least a $(1-p-\varepsilon)$-prefix of the current window. We prove that it is impossible to decode more than a $(1-p)$-prefix of the window in the worst case, which makes our scheme optimal in this sense. Our scheme runs in polylogarithmic time in the size of the window (per transmitted element), causes constant communication overhead, and succeeds with overwhelming probability. The scheme assumes the parties preshare a long random string unknown to the channel. When the noisy channel is additive, we lift the shared randomness assumption and design a scheme that is resilient to levels of noise below $p<1/2$.

中文翻译：

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适用于滑动式Windows的高效纠错代码

SIAM离散数学杂志，第34卷，第1期，第904-937页，2020年1月。
我们考虑了在滑动窗口模型中传递（无限）数据流的任务，其中通信是在嘈杂的信道上进行的，其对抗替代噪声率为1。特别是，对于任何噪声级别$ {p <1} $和任何小的$ \ varepsilon> 0 $，我们都会设计一种有效的编码方案，使得只要滑动窗口中的有效噪声水平低于$ p $，接收器就至少解码$（1-p- \ varepsilon）当前窗口的$前缀。我们证明，在最坏的情况下，解码窗口的$（1-p）$前缀是不可能的，这在这种意义上使我们的方案最佳。我们的方案在窗口大小（每个传输元素）的多对数时间内运行，导致恒定的通信开销，并且以压倒性的概率成功。该方案假设各方预先共享了一个未知的长随机字符串。当嘈杂的信道是可加的时，我们取消共享随机性假设，并设计一种方案，可对低于$ p <1/2 $的噪声水平进行恢复。