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Marius Drechsler 2024-07-28 19:03:18 +02:00
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content/BACH.typ Normal file
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= Boundary Adaptive Clustering with Helper Data

19
content/SMHD.typ
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@ -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 of changing the temperature both during the enrollment and the reconstruction phase.
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.
==== 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.

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@ -1,595 +1,99 @@
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5,40,0.08442914999999998
5,41,0.08443169999999998
5,42,0.08446025000000003
5,43,0.08444170000000001
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694
data/errorrates/2bit_temp/reconstruction/errorrates_left_25_35.csv
View file

@ -1,595 +1,99 @@
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@ -1,595 +1,99 @@
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4,99,0.078605625
5,1,0.1674046
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5,3,0.15482524999999997
5,4,0.15420894999999996
5,5,0.1539352
5,6,0.15379235000000002
5,7,0.15364825
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5,11,0.15336945000000002
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5,13,0.15329779999999996
5,14,0.15331765
5,15,0.15334525000000002
5,16,0.15323145
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5,18,0.15321535
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5,22,0.15324780000000002
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5,24,0.15323815
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5,27,0.15321690000000002
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5,41,0.15321419999999997
5,42,0.15323165000000002
5,43,0.15323265000000003
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5,45,0.1532384
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1,0.039957
2,0.002101
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3 1 3 2 0.0005485 0.000008249999999999999
4 1 4 3 0.000355625 0.000006000000000000002
5 1 5 4 0.00028875 0.0000065000000000000004
6 1 6 5 0.000226625 0.0000055000000000000016
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91 1 91 90 0.000148625 0.00000625
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97 1 97 96 0.000157625 0.00000625
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99 1 99 98 0.00015275 0.00000625
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694
data/errorrates/2bit_temp/reconstruction/errorrates_left_25_55.csv
View file

@ -1,595 +1,99 @@
bit,metric,errorrate
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45
graphics/plots/temperature/25_5_re.typ Normal file
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@ -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)))
})
})

BIN
main.pdf
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1
main.typ
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@ -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"