Sequence Reconstruction Over Coloring Channels for Protein Identification

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.