From 0ab044355e7dfadd645faa184623a0ded644eaef Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Wed, 7 Aug 2024 17:27:43 +0200 Subject: [PATCH] BACH Start --- content/SMHD.typ | 11 +++-------- .../quantizers/bach/sign-based-overlay.typ | 10 ++++++++-- main.pdf | Bin 1189232 -> 1196346 bytes 3 files changed, 11 insertions(+), 10 deletions(-) diff --git a/content/SMHD.typ b/content/SMHD.typ index 0640d32..df6064c 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -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. 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. -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 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 $100 "metrics"$. 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. 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. 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 diff --git a/graphics/quantizers/bach/sign-based-overlay.typ b/graphics/quantizers/bach/sign-based-overlay.typ index e53eea1..a9ae873 100644 --- a/graphics/quantizers/bach/sign-based-overlay.typ +++ b/graphics/quantizers/bach/sign-based-overlay.typ @@ -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 dashed = (stroke: (dash: "dashed")) @@ -15,7 +17,11 @@ y-min: 0, y-max: 1,{ plot.add(((-3,0), (0,0), (0,1), 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