On the Capacity of DNA Labeling in the Single-Label Setting
This study addresses the long-standing open problem of computing the capacity and constructing optimal codes for single-tag labeling of DNA sequences. By modeling the labeling process as a deterministic channel, this work establishes, for the first time, an equivalence between the labeling capacity and the zero-error capacity of star graphs, conducting a systematic analysis that integrates information-theoretic, graph-theoretic, and combinatorial coding techniques. The authors fully derive the zero-error capacities of all star graphs and precisely characterize the labeling capacity for all single-tag scenarios over arbitrary finite alphabets. Furthermore, they present a universal coding construction scheme that achieves this capacity and delineate the capacity bounds along with their extremal structures for fixed tag lengths. These contributions collectively provide a complete theoretical resolution to the fundamental limits of single-tag DNA labeling.