Capacity of DNA Data Embedding Under Substitution Mutations

A number of methods have been proposed over the
last decade for encoding information using deoxyribonucleic acid
(DNA), giving rise to the emerging area of DNA data embedding.
Since a DNA sequence is conceptually equivalent to a sequence
of quaternary symbols (bases), DNA data embedding (diversely
called DNA watermarking or DNA steganography) can be seen
as a digital communications problem where channel errors are
analogous to mutations of DNA bases. Depending on the use of
coding or noncoding DNA host sequences, which respectively
denote DNA segments that can or cannot be translated into
proteins, DNA data embedding is essentially a problem of
communications with or without side information at the encoder.
In this paper the Shannon capacity of DNA data embedding
is obtained for the case in which DNA sequences are subject
to substitution mutations modelled using the Kimura model
from molecular evolution studies. Inferences are also drawn
with respect to the biological implications of some of the results
presented.