26 lines
3 KiB
XML
26 lines
3 KiB
XML
= Conclusion and Outlook
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During the course of this work, we took a closer look at an already introduced @hda, @smhdt and provided a concrete realization.
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Our experiments showed that after a certain point, using more metrics $S$ won't improve the @ber any further as they behave asymptotically for $S arrow infinity$.
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Furthermore, we concluded that for higher choices of the symbol width $M$, @smhdt will not be able to improve on the @ber, as the initial error is too high.
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An interesting addition to our analysis provided the improvement of Gray-coded labelling for the quantizer as this resulted in an improvement of $approx 30%$.
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Going on, we introduced the idea of a new @hda which we called Boundary Adaptive Clustering with Helper data @bach.
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Here we aimed to utilize the idea of moving our initial @puf measurement values away from the quantizer bound to reduce the @ber using weighted linear combinations of our input values.
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Although this method posed promising results for a sign-based quantization yielding an improvement of $approx 96%$ in our testing, finding a good approach to generalize this concept turned out to be difficult.
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The first issue was the lack of an analytical description of the probability distribution resulting from the linear combinations.
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We accounted for that by using an algorithm that alternates between defining the quantizing bounds using an @ecdf and optimizing the weights for the linear combinations based on the found bounds.
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The loose definition of @eq:optimization to find an ideal linear combination which maximizes the distance to its nearest quantization bound did not result in a stable probability distribution over various iterations.
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Thus, we proposed a different approach to approximate the linear combination to the centers between the quantizing bounds.
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This method resulted in a stable probability distribution, but did not provide any meaningful improvements to the @ber in comparison to not using any helper data at all.
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Future investigations of the @bach idea might find a solution to the convergence of the bound distance maximization strategy.
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Since the vector of bounds $bold(b)$ is updated every iteration of @bach, a limit to the deviation from the previous position of a bound might be set.
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Furthermore, a recursive approach to reach higher order bit quantization inputs might also result in a converging distribution.
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If we do not want to give up the approach using a vector of optimal points $bold(cal(o))$ as in the center point approximation, a way may be found to increase the distance between all optimal points $bold(cal(o))$ to achieve a better separation for the results of the linear combinations in every quantizer bin.
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If a converging realization of @bach is found, using fractional weights instead of $plus.minus 1$ could provide more flexibility for the outcome of the linear combinations.
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Ultimately, we can build on this in the future and provide a complete key storage system using @bach or @smhdt to improve the quantization process.
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But in the end, the real quantizers were the friends we made along the way.
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