Sequence Reconstruction over Coloring Channels for Protein Identification

TL;DR

This paper introduces a novel coloring channel model inspired by protein identification, analyzing its information capacity and optimal configurations using combinatorial design theory.

Contribution

It extends the sequence reconstruction problem by defining coloring channels and characterizes optimal profiles via 2-covering designs, providing bounds on their covering numbers.

Findings

Optimal coloring profiles correspond to 2-covering designs.

The minimal covering number for maximum information rate is identified.

Conditions for the optimality of any coloring profile are established.

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.