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.