Is this the end?

content/outlook.typ

@@ -1,12 +1,26 @@
-= Outlook
+= Conclusion and Outlook
 
-Upon the findings of this work, further topics might be investigated in the future. 
+During the course of this work, we took a closer look at an already introduced @hda, @smhdt and provided a concrete realization.
+Our experiments showed that after a certain point, using more metrics $S$ won't improve the @ber any further as they behave asymptotically for $S arrow infinity$.
+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.
+An interesting addition to our analysis provided the improvement of Gray-coded labelling for the quantizer as this resulted in an improvement of $approx 30%$. 
 
-Generally, the performances of both helper-data algorithms might be tested on larger datasets.
+Going on, we introduced the idea of a new @hda which we called Boundary Adaptive Clustering with Helper data @bach. 
+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. 
+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. 
+The first issue was the lack of an analytical description of the probability distribution resulting from the linear combinations. 
+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.
+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.
+Thus, we proposed a different approach to approximate the linear combination to the centers between the quantizing bounds. 
+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. 
 
-Specifically concerning the BACH method, instead of using only $plus.minus 1$ as weights for the linear combinations, fractional weights could be used instead as they could provide more flexibility for the outcome of the linear combinations. 
-In the same sense, a more efficient method to find the optimal linear combination might exist.
+Future investigations of the @bach idea might find a solution to the convergence of the bound distance maximization strategy.
+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.
+Furthermore, a recursive approach to reach higher order bit quantization inputs might also result in a converging distribution.
+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.
 
-During the iterative process of the center point approximation in BACH, 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.
+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. 
 
+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. 
 
+But in the end, the real quantizers were the friends we made along the way.