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Educational Programme
Final Grade
Year of Graduation
Valeriya Potapova
Signature Сodes for a Сlass of Multiple-Access Channels
Data Science
(Master’s programme)
In this paper we have investigated the mathematical problem of steganography and its applications at

length. We have seen the dierent models (the active warden and the passive warden) and some methods

to solve the problem. Two approaches (algebraic and probabilistic) were examined, and we have seen that

there is a link between the problem of steganography and coding theory. To be exact, there is an equivalence

between stego schemes and covering codes. So we monitored articles that propose the ways to construct

eective covering codes.

The particular problem of writing on dirty (and wet) paper was investigated. We have analyzed the perfor-

mance of one interesting algorithm (ZZW) and proposed its improvement.

In addition we have analyzed one important asymptotically optimal perfect stego scheme and its behavior

in the noisy channel. It turns out that this scheme is perfect only in perfect environment and some curious

errors occur in the messages during the transmission via a noisy channel (or a channel with a warden).

To correct the aforementioned errors we need codes correcting deletions and insertions of symbols, but at

nowadays there are codes correcting only one error of that type. Because of unsolved problems of additive

number theory we can not construct codes that correct more insertions and deletions.

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