On the embedding capacity of DNA strands under insertion, deletion and substitution mutations

A number of methods have been proposed over the last decade for embedding information within deoxyribonucleic acid (DNA). Since a DNA sequence is conceptually equivalent to a unidimensional digital signal, DNA data embedding (diversely called DNA watermarking or DNA steganography) can be seen either as a traditional communications problem or as an instance of communications with side information at the encoder, similar to data hiding. These two cases correspond to the use of noncoding or coding DNA hosts, which, respectively, denote DNA segments that cannot or can be translated into proteins. A limitation of existing DNA data embedding methods is that none of them have been designed according to optimal coding principles. It is not possible either to evaluate how close to optimality these methods are without determining the Shannon capacity of DNA data embedding. This is the main topic studied in this paper, where we consider that DNA sequences may be subject to substitution, insertion, and deletion mutations.