From 429df6bc68758b604ebe656c1d2e5cbcd141b994 Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Thu, 25 Jul 2024 20:07:20 +0200 Subject: [PATCH] Continued on analysis, almost finished with chapter!! --- content/SMHD.typ | 38 ++ data/1bit.csv | 94 +++ .../reconstruction/errorrates_left_25_25.csv | 595 ++++++++++++++++++ .../reconstruction/errorrates_left_25_35.csv | 595 ++++++++++++++++++ .../reconstruction/errorrates_left_25_5.csv | 595 ++++++++++++++++++ .../reconstruction/errorrates_left_25_55.csv | 595 ++++++++++++++++++ graphics/plots/1bit_obs.typ | 20 + graphics/plots/errorrates_changerate.typ | 16 + main.pdf | Bin 732303 -> 742404 bytes 9 files changed, 2548 insertions(+) create mode 100644 data/1bit.csv create mode 100644 data/errorrates/2bit_temp/reconstruction/errorrates_left_25_25.csv create mode 100644 data/errorrates/2bit_temp/reconstruction/errorrates_left_25_35.csv create mode 100644 data/errorrates/2bit_temp/reconstruction/errorrates_left_25_5.csv create mode 100644 data/errorrates/2bit_temp/reconstruction/errorrates_left_25_55.csv create mode 100644 graphics/plots/1bit_obs.typ create mode 100644 graphics/plots/errorrates_changerate.typ diff --git a/content/SMHD.typ b/content/SMHD.typ index da9ed9d..3c591c5 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -344,6 +344,8 @@ The here proposed S-Metric Helper Data Method can be improved by using gray code @fig:2-bit-gray shows a 2-bit quantizer with gray coded labelling. In this example, we have an advantage at $tilde(x) = ~ 0.5$, because a quantization error only returns one wrong bit instead of two. +== Helper data volume + == Experiments & Results We tested the implementation of @sect:smhd_implementation with the temperature dataset of @dataset. @@ -363,4 +365,40 @@ For this analysis, enrollment and reconstruction were both performed at room tem caption: [Bit error rates for same temperature execution] ) +We can observe two key properties of the S-Metric method in @fig:global_errorrates. +The error rate in this plot is scaled logarithmically.\ +The exponential growth of the error rate of classic 1-metric configurations can be observed through the linear increase of the error rates. +Also, as we expanded on in @par:offset_props, using more metrics will, at some point, not further improve the bit error rate of the key. +At a symbol width of $m >= 6$ bits, no further improvement through the S-Metric method can be observed. + +#figure( + include("../graphics/plots/errorrates_changerate.typ"), + caption: [Asymptotic performance of S-Metric] +) + +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 $phi$ + +//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 + +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. + +==== Different reconstruction temperature + + +==== Different enrollment temperature + 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+6,99,0.23480129166666663 diff --git a/graphics/plots/1bit_obs.typ b/graphics/plots/1bit_obs.typ new file mode 100644 index 0000000..ec6d0e4 --- /dev/null +++ b/graphics/plots/1bit_obs.typ @@ -0,0 +1,20 @@ +#import "@preview/cetz:0.2.2": canvas, plot + +#let data = csv("../../data/1bit.csv") +#let ndata = data.map(value => value.map(v => float(v)))// fucking hell is that cursed + +#let dashed = (stroke: (dash: "dashed")) +#canvas({ + plot.plot(size: (10,1), + x-tick-step: none, + x-ticks: ((1, [1]), (2, [2]), (3, [3]), (4, [4]), (5, [5]), (6, [6])), + y-label: $E(1)$, + x-label: $m$, + y-tick-step: 500, + axis-style: "left", + x-min: 0, + y-max: 1, + { + plot.add((ndata), mark: "o", mark-size: 0.0001) + }) +}) diff --git a/graphics/plots/errorrates_changerate.typ b/graphics/plots/errorrates_changerate.typ new file mode 100644 index 0000000..9314d7e --- /dev/null +++ b/graphics/plots/errorrates_changerate.typ @@ -0,0 +1,16 @@ +#import "@preview/cetz:0.2.2": canvas, plot + +#let dashed = (stroke: (dash: "dashed")) +#canvas({ + plot.plot(size: (10,4), + x-tick-step: none, + x-ticks: ((1, [1]), (2, [2]), (3, [3]), (4, [4]), (5, [5]), (6, [6])), + y-label: $(x_"1" (m)) / (x_"100" (m))$, + x-label: $m$, + y-tick-step: 500, + axis-style: "left", + x-min: 0, + { + plot.add(((1,1815.2), (2,660), (3,46), (4,3.11), (5,1.33), (6,1.07)), mark: "o") + }) +}) diff --git a/main.pdf b/main.pdf index b4574e33cf3cf933a76d2d1a7a62444d3ab3469e..2fadeffef8485f33b97d7332570e87d93bd2f1ce 100644 GIT binary patch delta 207500 zcmeCbsnfDTS5P&;#ZA{x&zwuOp`oFHi_2*G!zgx<=>~qxEYlx&GApnJhK2d~`cL$C zmoif@PzZ|UQc%zj$q&uTOwLb9RWPyu2~M8CtU6txjaeP8T6VHLV-}7#N#wwqw7^G+8^8Z~Fg4PIgv9OH(tW$%b48^=o6Zyf>A-+!mGfcJ0!u zx7Hrr{pQHD+>;yM+$f5^JMGrRXVX%StEsf<2+J@fp0;7)oOhguM}Y0{28)wE2@(l2 z7@FnzKUF-a{KnFj-)1o3d)pbNjeq|7ht7R>?U71L<^K28``e!s&0n`Fy7bkRo3BEy zPBmx|kbE>}L+9e%-%YpK)PGnucj<|rl9w)ie0ku`?)&jY4jhlg6yMyJwcna>(=7Fm zy_1E`lzdw|bHlquum2R*%y*faEZq3hGEiYstH&?3Q=8S6os-%BiSvAE&3>gLcbX?J 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