On the Capacity of Sequences of Coloring Channels

Wenjun Yu; Moshe Schwartz

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arXiv · 2604.08234

On the Capacity of Sequences of Coloring Channels

Wenjun Yu·Moshe Schwartz

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Abstract

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.

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Wenjun Yu, Moshe Schwartz. 2026-04-09. On the Capacity of Sequences of Coloring Channels. https://arxiv.org/abs/2604.08234

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