DNA labeling is a powerful tool in molecular biology and biotechnology that allows for the visualization, detection, and study of DNA at the molecular level. Under this paradigm, a DNA molecule is being labeled by specific k patterns and is then imaged. Then, the resulted image is modeled as a (k + 1)- ary sequence in which any non-zero symbol indicates on the appearance of the corresponding label in the DNA molecule. The primary goal of this work is to study the labeling capacity, which is defined as the maximal information rate that can be obtained using this labeling process. The labeling capacity is computed for any single label and several results are provided for multiple labels as well. Moreover, we provide the optimal minimal number of labels of length one or two that are needed in order to gain labeling capacity of 2.

翻译：DNA标记是分子生物学和生物技术中一项强大的工具，可在分子层面实现DNA的可视化、检测与研究。在该范式下，DNA分子通过特定的k个模式进行标记，随后进行成像。所得图像被建模为(k+1)元序列，其中任何非零符号均表示对应标记在DNA分子中出现。本研究的主要目标是探究标记容量，即通过此标记过程所能获得的最大信息速率。针对任意单一标记，我们计算了其标记容量，并同时给出了多标记情况下的若干结果。此外，我们提供了获得2容量所需的最优最小标记数量，这些标记长度为1或2。