A considerable amount of attention has been lately payed to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper supplies a fair comparison between significant representatives of both this family of methods and the former spread-spectrum approaches that make use of near-optimal ML decoding; the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions. Accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of Monte Carlo simulations. For Dithered Modulation (DM) a novel technique that allows to obtain tighter bounds to the probability of error is presented. Within the new framework, the strong points and weaknesses of both methods are distinctly displayed. This comparative study allows us to propose a new technique named "Quantized Projection" (QP), which by adequately combining elements of those previous approaches, produces gains in performance.

BackgroundIn recent times, the application of deoxyribonucleic acid (DNA) has diversified with the emergence of fields such as DNA computing and DNA data embedding. DNA data embedding, also known as DNA watermarking or DNA steganography, aims to develop robust algorithms for encoding non-genetic information in DNA. Inherently DNA is a digital medium whereby the nucleotide bases act as digital symbols, a fact which underpins all bioinformatics techniques, and which also makes trivial information encoding using DNA straightforward. However, the situation is more complex in methods which aim at embedding information in the genomes of living organisms. DNA is susceptible to mutations, which act as a noisy channel from the point of view of information encoded using DNA. This means that the DNA data embedding field is closely related to digital communications. Moreover it is a particularly unique digital communications area, because important biological constraints must be observed by all methods. Many DNA data embedding algorithms have been presented to date, all of which operate in one of two regions: non-coding DNA (ncDNA) or protein-coding DNA (pcDNA).ResultsThis paper proposes two novel DNA data embedding algorithms jointly called BioCode, which operate in ncDNA and pcDNA, respectively, and which comply fully with stricter biological restrictions. Existing methods comply with some elementary biological constraints, such as preserving protein translation in pcDNA. However there exist further biological restrictions which no DNA data embedding methods to date account for. Observing these constraints is key to increasing the biocompatibility and in turn, the robustness of information encoded in DNA.ConclusionThe algorithms encode information in near optimal ways from a coding point of view, as we demonstrate by means of theoretical and empirical (in silico) analyses. Also, they are shown to encode information in a robust way, such that mutations have isolated effects. Furthermore, the preservation of codon statistics, while achieving a near-optimum embedding rate, implies that BioCode pcDNA is also a near-optimum first-order steganographic method.

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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 tantamount to mutations of DNA bases. Depending on the use of coding or noncoding DNA hosts, 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.

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