Final changes

content/BACH.typ

@@ -295,7 +295,7 @@ We can lower the computational complexity of this approach by using the assumpti
 The end result of $bold(cal(o))$ can be calculated once for a specific device series and saved in the ROM of. 
 During enrollment, only the vector $bold(h)_"opt"$ has to be calculated.
 
-=== Impact of helper-data volume and amount of addends
+=== Helper-data size and amount of addends
 
 The amount of helper data is directly linked to the symbol bit width $M$ and the amount of addends $N$ used in the linear combination.
 Because we can set the first helper data bit $h_1$ of a linear combination to $1$ to omit the random choice, the resulting extracted bit to helper data bit ratio $cal(r)$ can be defined as $cal(r) = frac(M, N-1)$, whose equation is similar tot he one we used in the @smhdt analysis.
@@ -391,10 +391,10 @@ We can also compare the performance of @bach using the center point approximatio
   caption: [#glspl("ber") for higher order bit quantization without helper data ]
 )<tab:no_hd>
 
-Unfortunately, the comparison of #glspl("ber") of @tab:no_hd[Tables] and @tab:BACH_performance[] shows that our current realization of @bach does either ties the @ber in @tab:no_hd or is worse.
+Unfortunately, the comparison of #glspl("ber") of @tab:no_hd[Tables] and @tab:BACH_performance[] shows that our current realization of @bach either ties the @ber in @tab:no_hd or is worse.
 Let's find out why this happens.
 
-==== Justification of the original idea
+==== Discussion
 
 If we take a step back and look at the performance of the optimized single-bit sign-based quantization process of @sect:1-bit-opt, we can compare the following #glspl("ber"):
 

content/introduction.typ

@@ -11,7 +11,7 @@ The general operation of a @puf with a @hda can be divided into two separate sta
 
 #figure(
   include("../charts/PUF.typ"), 
-  caption: [@puf model description using enrollment and reconstruction.]
+  caption: [@puf model description using enrollment and reconstruction @PUFChartRef]
 )<fig:puf_operation>
 
 The enrollment stage will usually be performed in near ideal, lab-like conditions i.e. at room temperature ($25°C$).
@@ -31,8 +31,7 @@ To achieve that, helper data is generated to define multiple quantizers for the
 A generalization outline to extend @tmhdt for higher order bit quantization has already been proposed by Fischer in @smhd.  
 
 In the course of this work, we will first take a closer look at @smhdt as proposed by Fischer @smhd and provide a concrete realization for this method.
-We will also propose a method to shape the input values of a @puf to better fit within the bounds of a multi-bit quantizer which we call @bach. 
-We will investigate the question which of these two #glspl("hda") provides the better performance for higher order bit cases with the least amount of helper data bits.
+We will also propose the idea of a method to shape the input values of a @puf to better fit within the bounds of a multi-bit quantizer which we call @bach and discuss how such a @hda can be successfully implemented in the future.
 
 == Notation
 

content/outlook.typ

@@ -10,7 +10,7 @@ Here we aimed to utilize the idea of moving our initial @puf measurement 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.
+The initial loose definition to find ideal linear combinations which maximize the distance to their nearest quantization bounds 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.