Mean-based reconstruction is a fundamental, natural approach to worst-case trace reconstruction over channels with synchronization errors. It is known that $\exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based worst-case trace reconstruction over the deletion channel, and this result was also extended to certain channels combining deletions and geometric insertions of uniformly random bits. In this work, we use a simple extension of the original complex-analytic approach to show that these results are examples of a much more general phenomenon: $\exp(O(n^{1/3}))$ traces suffice for mean-based worst-case trace reconstruction over any memoryless channel that maps each input bit to an arbitrarily distributed sequence of replications and insertions of random bits, provided the length of this sequence follows a sub-exponential distribution.

翻译：以平均为基础的重建是对同步错误的频道进行最坏情况追踪重建的一种基本、自然的方法,众所周知,美元(O(n)1/3})的痕迹对于在删除频道上进行以平均为基础的最坏情况追踪重建是必要的,而且足够在删除频道上进行以平均为基础的最坏情况追踪重建,而且这一结果还扩大到某些将删除和统一随机位数的几何插入结合起来的渠道。在这项工作中,我们使用原始的复杂分析方法简单扩展,以表明这些结果是一个更普遍现象的例子:$(O(n)1/3})美元(美元)的痕迹足以用来在任何无记忆的频道上进行以平均方式进行最坏情况追踪重建,而每个输入点绘制任意分布的复制和随机位数插入的顺序,只要该顺序的长度遵循亚加速分布。