Sequence Reconstruction over Coloring Channels for Protein Identification
Information Theory
2025-08-05 v1 math.IT
Abstract
This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed subset (the coloring) of the alphabet. By extending this to a coloring profile, a tuple of distinct colorings, we analyze the channel's information rate and capacity. We prove that optimal (i.e., achieving maximum information rate) coloring profiles correspond to 2-covering designs and identify the minimal covering number required for maximum information rate, as well as the minimum number for which any coloring profile is optimal.
Cite
@article{arxiv.2508.02229,
title = {Sequence Reconstruction over Coloring Channels for Protein Identification},
author = {Jessica Bariffi and Antonia Wachter-Zeh and Eitan Yaakobi},
journal= {arXiv preprint arXiv:2508.02229},
year = {2025}
}