Embedding techniques typically provide a collection of variant locations in the document, each of which provides a choice between a few variants that are equivalent to the user.

This is true also outside the plotted range. Doing this we can make two kinds of errors: Fingerprinting, watermarking, copyright protection 1 Introduction Fingerprinting of digital data is a possible solution to the problem of copyright violations.

We want the probability of both of these errors to be small, and this leads to a trade-off between conflicting goals. If we instead, by choosing appropriate fingerprint lengths, try to fix the error probabilities we can see how the fingerprint length needed for a certain error probability, Niclas wiberg thesis with the number of pirates.

The curves are, from the left: In this section, we describe what we mean by fingerprinting and attacks against it. The probabilities of making these two kinds of errors are of course interesting and we will find expressions for them in the following.

We also define and describe some of the terminology used by us and others when discussing fingerprinting. In each location the two variants should be equivalent and the nature of the variants and their locations Niclas wiberg thesis not be detectable by a user.

Ideally, given a recovered fingerprint z, we would like to identify all the involved pirates. Proceedings of Crypto 95, Springer-Verlag, pp.

It can only be Niclas wiberg thesis for testing whether or not a certain, proposed group of users should be considered guilty of having created a certain illegal copy. Only in these variant locations are the pirates forced in their choice of which bit value to put in their illegally created copy, since they do not know the embedded appearance of the other bit value.

The right end-points of the curves correspond to the lowest possible probabilities of failing to accuse a guilty group, for that specific combination of c and n. In this case this means accusing a group that is not guilty and failing to accuse a group that is guilty.

The probability that r will be close to N will be small, and it will tend to 0 as N grows. Ifthe group is innocent, r will be an outcome of a random variable taken from a binomial distribution, r Bi N, 2 1. The number of pirates are 2, 3, The purpose of fingerprinting is to make a number of otherwise identical copies unique, so that if an illegally made copy is found, it is possible to trace the person or persons who made it.

By choosing the value of N t it is possible to choose the combination of error probabilities from the points on the curve corresponding to the value of c and n for the group under consideration. In the method described, we only take into account the undetectable locations.

The main reason for this is that it is mathematically relatively easy to deal with. In figure 1 below we see the possible trade-offs for different numbers of pirates and different fingerprint lengths.

It is 5 8 important to remember though, that this is a testing method, not a tracing method. This can be done by first recovering the fingerprint of the illegal copy and then comparing that fingerprint with a database of all users fingerprints.

If several users with different copies of the document work together to create and redistribute an illegal copy, using some combination of their copies, they are called a collusion of pirates. The reason for this is that under the marking assumption the pirates have no freedom of choice in these locations.

Both of these binomially distributed, random variables have their origin in the fact that all users fingerprints are random see subsection 1. We have chosen to consider binary random fingerprints with each bit drawn independently and with equal probability of zero and one.

The output from the method is thus a flag saying guilty or not guilty. Probability of failing to accuse a guilty group Probability of accusing an innocent group Figure 1. The performance of random fingerprinting in conjunction with a specific testing method is analyzed.

The coding should be resistant against active attacks by pirates. In other words, fingerprinting only works if some kind of alteration or distortion is allowed. These alterations can be managed by some embedding technique, such as choosing between synonyms in certain locations.List of computer science publications by Niclas Wiberg.

In this thesis, it is showed that many iterative decoding algorithms are special cases of two generic algorithms, the min-sum and sum-product algorithms, which also. AT THE close nine errors to avoid in composing a thesis of the nike business ethics essay first World War, when I was a student at Cornell, I took a course called English 8.

PART I: niclas wiberg thesis AN INTRODUCTION TO COLLEGE COMPOSITION., ) Richard Carrier.

Iterative decoding occurs when the Tanner graph has cycles (e.g., turbo codes); the resulting algorithms are in general suboptimal, but signiﬁcant complexity reductions are possible compared to.

Niclas Wiberg A factor graph is a bipartite graph that expresses how a global function of several variables factors into a product of local functions. Factor graphs subsume many other graphical models, including Bayesian networks, Markov random fields, and Tanner graphs.

Wiberg thesis.

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