More on analysis

2024-07-28 19:03:18 +02:00 · 2024-07-28 19:03:18 +02:00 · 4346630b65
commit 4346630b65
parent 429df6bc68
11 changed files with 657 additions and 2385 deletions
--- a/content/BACH.typ
+++ b/content/BACH.typ
@ -0,0 +1,3 @@
 = Boundary Adaptive Clustering with Helper Data
--- a/content/SMHD.typ
+++ b/content/SMHD.typ
@ -332,7 +332,7 @@ lim_(s arrow.r infinity) phi_"max,odd" &= frac(s-1, 2^n dot s dot 4) #<eq:offset
 &= frac(1, 2^n dot 4) = phi_"max,even" 
 $
-== Improvements
+== Improvements<sect:smhd_improvements>
 The here proposed S-Metric Helper Data Method can be improved by using gray coded labels for the quantized symbols instead of naive ones @smhd.
 #align(center)[
@ -391,14 +391,23 @@ From $m >= 6$ onwards, $(x_"1" (m)) / (x_"100" (m))$ approaches $~1$, which mean
 === Impact of temperature
-Usually we will perform enrollment at room temperature. 
+We will now take a look at the impact on the error rates of changing the temperature both during the enrollment and the reconstruction phase.
 We will now take a look at the impact of changing the temperature both during the enrollment and the reconstruction phase.
-==== Different reconstruction temperature
+The most common case to look at, is if we consider a fixed temperature during enrollment, most likely $25°C$.
 Since we wont always be able to recreate lab-like conditions during the reconstruction phase, it makes sense to look at the error rates at which reconstruction was performed at different temperatures. 
 #figure(
  include("../graphics/plots/temperature/25_5_re.typ"),
  caption: [Reconstruction at different temperatures]
 )<fig:smhd_tmp_reconstruction>
@fig:smhd_tmp_reconstruction shows the results of this experiment conducted with a 2-bit configuration.\
 As we can see, the further we move away from the temperature of enrollment, the higher the bit error rates turns out to be.
 // Table here with BER without helper data and with 100 metrics for best improvement case. Talk about improvements in numerical parts
 ==== Different enrollment temperature
 === Gray coding
 In @sect:smhd_improvements, we discussed how a gray coded labelling for the quantizer could improve the bit error rates of the S-Metric method.
--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_15.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_15.csv
@ -0,0 +1,99 @@
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--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_25.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_25.csv
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--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_35.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_35.csv
@ -1,595 +1,99 @@
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--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_45.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_45.csv
@ -0,0 +1,99 @@
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--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_5.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_5.csv
@ -1,595 +1,99 @@
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--- a/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_55.csv
+++ b/data/errorrates/2bit_temp/reconstruction/errorrates_left_25_55.csv
@ -1,595 +1,99 @@
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 4,91,0.11505962500000001
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 5,83,0.18601074999999992
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 5,99,0.18601654999999997
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 6,16,0.23479775000000008
 6,17,0.23478379166666674
 6,18,0.23481016666666665
 6,19,0.23480679166666665
 6,20,0.2348085
 6,21,0.23479224999999995
 6,22,0.23477374999999995
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 6,24,0.23481379166666663
 6,25,0.23477912499999995
 6,26,0.23479675000000003
 6,27,0.23481849999999999
 6,28,0.23472566666666658
 6,29,0.23479000000000003
 6,30,0.2347575
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 6,96,0.2347874583333333
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 6,98,0.23479187499999996
 6,99,0.23480129166666663
--- a/graphics/plots/temperature/25_5_re.typ
+++ b/graphics/plots/temperature/25_5_re.typ
@ -0,0 +1,45 @@
 #import "@preview/cetz:0.2.2": canvas, plot
 #let data5 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_5.csv")
 #let ndata5 = data5.map(value => value.map(v => calc.log(float(v))))// fucking hell is that cursed
 #let data25 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_25.csv")
 #let ndata25 = data25.map(value => value.map(v => calc.log(float(v))))
 #let data35 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_35.csv")
 #let ndata35 = data35.map(value => value.map(v => calc.log(float(v))))
 #let data55 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_55.csv")
 #let ndata55 = data55.map(value => value.map(v => calc.log(float(v))))
 #let data15 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_15.csv")
 #let ndata15 = data15.map(value => value.map(v => calc.log(float(v))))
 #let data45 = csv("../../../data/errorrates/2bit_temp/reconstruction/errorrates_left_25_45.csv")
 #let ndata45 = data45.map(value => value.map(v => calc.log(float(v))))
 #let formatter(v) = [$10^#v$]
 #let dashed = (stroke: (dash: "dashed"))
 #canvas({
  plot.plot(size: (10,5),
    x-tick-step: none,
    //x-ticks: ((1, [1]), (2, [2]), (3, [3]), (4, [4]), (5, [5]), (6, [6])),
    y-label: $"Bit error rate"$,
    x-label: $s$,
    y-tick-step: 1,
    //y-ticks : (
    //  (-1.5, calc.exp(-1.5)),
    //),
    y-max: -1,
    y-format: formatter,
    axis-style: "left",
    {
    plot.add((ndata5), line: "spline", label: $5°C$)
    plot.add((ndata25), line: "spline", label: $25°C$)
    plot.add((ndata15), line: "spline", label: $15°C$)
    plot.add((ndata35), line: "spline", label: $35°C$)
    plot.add((ndata45), line: "spline", label: $45°C$)
    plot.add((ndata55), line: "spline", label: $55°C$, style: (stroke: (paint: teal)))
  })
 })
--- a/main.pdf
+++ b/main.pdf
--- a/main.typ
+++ b/main.typ
@ -31,6 +31,7 @@
 #include "content/introduction.typ"
 #include "content/SMHD.typ"
 #include "content/BACH.typ"
 //#include "content/state.typ"
 //#include "content/implementation.typ"
 //#include "content/benchmarks.typ"
		`@ -0,0 +1,3 @@`
							`= Boundary Adaptive Clustering with Helper Data`