Gene Tagging and the Data Hiding Rate

We analyze the maximum number of ways in which one can intrinsically tag
a very particular kind of digital asset: a gene, which is just a DNA sequence that encodes
a protein. We consider gene tagging under the most relevant biological constraints:
protein encoding preservation with and without codon count preservation. We show
that our finite and deterministic combinatorial results are asymptotically—as the length
of the gene increases— particular cases of the stochastic Gel’fand and Pinsker capacity
formula for communications with side information at the encoder, which lies at the
foundations of data hiding theory. This is because gene tagging is a particular case of
DNA watermarking.