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Marius Drechsler 2024-08-07 17:27:43 +02:00
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11
content/SMHD.typ
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@ -365,11 +365,11 @@ The dataset contains counts of positives edges of a toggle flip flop at a set ev
Because we want to analyze the performance of the S-Metric method over different temperatures, both during enrollment and reconstruction, we are limited to the second part of the experimental measurements of @dataset. Because we want to analyze the performance of the S-Metric method over different temperatures, both during enrollment and reconstruction, we are limited to the second part of the experimental measurements of @dataset.
We will have measurements of $50$ FPGA boards available with $1600$ and $1696$ ring oscillators each. To obtain the values to be processed, we subtract them in pairs, yielding $800$ and $848$ ring oscillator frequency differences _df_.\ We will have measurements of $50$ FPGA boards available with $1600$ and $1696$ ring oscillators each. To obtain the values to be processed, we subtract them in pairs, yielding $800$ and $848$ ring oscillator frequency differences _df_.\
Since the frequencies _f_ are normal distributed, the difference _df_ can be assumed to be zero-mean Gaussian distributed. Since the frequencies _f_ are normal distributed, the difference _df_ can be assumed to be zero-mean Gaussian distributed.
To apply the values _df_ to our implementation of the S-Metric method, we will first transform them into the Tilde-Domain using an inverse CDF, resulting in uniform distributed values $tilde(italic("df"))$. To apply the values _df_ to our implementation of the S-Metric method, we will first transform them into the Tilde-Domain using an inverse CDF, resulti/invite <mxid>ng in uniform distributed values $tilde(italic("df"))$.
Our resulting dataset consists of #glspl("ber") for quantization symbol widths of up to $6 "bits"$ evaluated with generated helper-data from up to $100 "metrics"$. Our resulting dataset consists of #glspl("ber") for quantization symbol widths of up to $6 "bits"$ evaluated with generated helper-data from up to $100 "metrics"$.
We chose not to perform simulations for bit widths higher than $6 "bits"$, as we will see later that we have already reached a bit error rate of approx. $10%$ for these configurations. We chose not to perform simulations for bit widths higher than $6 "bits"$, as we will see later that we have already reached a bit error rate of approx. $10%$ for these configurations.
=== Discussion === Results & Discussion
The bit error rate of different S-Metric configurations for naive labelling can be seen in @fig:global_errorrates. The bit error rate of different S-Metric configurations for naive labelling can be seen in @fig:global_errorrates.
For this analysis, enrollment and reconstruction were both performed at room temperature and the quantizer was naively labelled. For this analysis, enrollment and reconstruction were both performed at room temperature and the quantizer was naively labelled.
@ -394,14 +394,9 @@ This tendency can also be shown through @fig:errorrates_changerate.
Here, we calculated the quotient of the bit error rate using one metric and 100 metrics. Here, we calculated the quotient of the bit error rate using one metric and 100 metrics.
From $m >= 6$ onwards, $(x_"1" (m)) / (x_"100" (m))$ approaches $~1$, which means, no real improvement is possible anymore through the S-Metric method. From $m >= 6$ onwards, $(x_"1" (m)) / (x_"100" (m))$ approaches $~1$, which means, no real improvement is possible anymore through the S-Metric method.
//=== Observation of offset $phi$ === Helper Data Volume Trade-off
//If we take a look at the 1-bit case, we can nicely observe the approximating nature of $phi_"max,odd"$ to $phi_"max,even"$ of @par:offset_props.
//#figure(
// include("../graphics/plots/1bit_obs.typ"),
// caption: [Yoink]
//)
=== Impact of temperature<sect:impact_of_temperature> === Impact of temperature<sect:impact_of_temperature>

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graphics/quantizers/bach/sign-based-overlay.typ
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@ -1,4 +1,6 @@
#import "@preview/cetz:0.2.2": canvas, plot #import "@preview/cetz:0.2.2": *
#let line_style = (stroke: (paint: black, thickness: 2pt)) #let line_style = (stroke: (paint: black, thickness: 2pt))
#let dashed = (stroke: (dash: "dashed")) #let dashed = (stroke: (dash: "dashed"))
@ -15,7 +17,11 @@
y-min: 0, y-min: 0,
y-max: 1,{ y-max: 1,{
plot.add(((-3,0), (0,0), (0,1), (3,1)), style: line_style) plot.add(((-3,0), (0,0), (0,1), (3,1)), style: line_style)
plot.add(plot.sample-fn(
(x) => 1/calc.sqrt(2*calc.pi)*calc.exp(-(calc.pow(x,2)/2)),
(-3, 3),
300
))
}) })
}) })

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main.pdf
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