A single coloring channel is defined by a subset of letters it allows to pass through, while deleting all others. A sequence of coloring channels provides multiple views of the same transmitted letter sequence, forming a type of sequence-reconstruction problem useful for protein identification and information storage at the molecular level. We provide exact capacities of several sequences of coloring channels: uniform sunflowers, two arbitrary intersecting sets, and paths. We also show how this capacity depends solely on a related graph we define, called the pairs graph. Using this equivalence, we prove lower and upper bounds on the capacity, and a tailored bound for a coloring-channel sequence forming a cycle. In particular, for an alphabet of size $4$, these results give the exact capacity of all coloring-channel sequences except for a cycle of length $4$, for which we only provide bounds.

翻译：单个染色信道由允许通过的字母子集定义，同时删除其余所有字母。染色信道序列提供同一传输字母序列的多个视图，形成一种序列重建问题，对分子层面的蛋白质识别和信息存储具有重要应用价值。我们给出了若干染色信道序列的精确容量：均匀向日葵结构、两个任意交集集合以及路径结构。同时证明了该容量仅取决于我们定义的关联图——配对图。基于这种等价关系，我们推导了容量的上下界，并针对构成环路的染色信道序列给出了定制化界。特别地，对于大小为$4$的字母表，这些结果给出了除长度为$4$的环路外所有染色信道序列的精确容量（我们仅为此环路提供了界值）。