From ea1d02ce9f1017f1a9f1ad50fed09a36b1f4845c Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Wed, 17 Jul 2024 21:26:25 +0200 Subject: [PATCH] Ported everything to typst now --- bibliography.bib | 46 +++-- content/SMHD.typ | 175 +++++++++++++++++- content/introduction.typ | 15 +- glossary.typ | 1 + graphics/quantizers/s-metric/2_2_en.typ | 30 +++ graphics/quantizers/s-metric/3_2_en.typ | 30 +++ .../quantizers/s-metric/s-metric-compar1.typ | 25 +++ .../quantizers/s-metric/s-metric-compar2.typ | 25 +++ ...o-metric-enroll.typ => two-bit-enroll.typ} | 0 graphics/quantizers/two-metric/enrollment.typ | 30 +++ .../quantizers/two-metric/example_enroll.typ | 27 +++ .../two-metric/example_reconstruct.typ | 27 +++ .../quantizers/two-metric/reconstruction.typ | 28 +++ main.pdf | Bin 488218 -> 500091 bytes main.typ | 10 +- 15 files changed, 439 insertions(+), 30 deletions(-) create mode 100644 graphics/quantizers/s-metric/2_2_en.typ create mode 100644 graphics/quantizers/s-metric/3_2_en.typ create mode 100644 graphics/quantizers/s-metric/s-metric-compar1.typ create mode 100644 graphics/quantizers/s-metric/s-metric-compar2.typ rename graphics/quantizers/{two-metric-enroll.typ => two-bit-enroll.typ} (100%) create mode 100644 graphics/quantizers/two-metric/enrollment.typ create mode 100644 graphics/quantizers/two-metric/example_enroll.typ create mode 100644 graphics/quantizers/two-metric/example_reconstruct.typ create mode 100644 graphics/quantizers/two-metric/reconstruction.typ diff --git a/bibliography.bib b/bibliography.bib index 6c12cc3..afb10df 100644 --- a/bibliography.bib +++ b/bibliography.bib @@ -1,23 +1,31 @@ -@article{quetschlich2023mqtbench, - title={{{MQT Bench}}: Benchmarking Software and Design Automation Tools for Quantum Computing}, - shorttitle={{MQT Bench}}, - journal={{Quantum}}, - author={Quetschlich, Nils and Burgholzer, Lukas and Wille, Robert}, - year={2023}, - note={{{MQT Bench}} is available at \url{https://www.cda.cit.tum.de/mqtbench/}}, +@inproceedings{tmhd1, + title={Two-metric helper data for highly robust and secure delay PUFs}, + author={Danger, Jean-Luc and Guilley, Sylvain and Schaub, Alexander}, + booktitle={2019 IEEE 8th International Workshop on Advances in Sensors and Interfaces (IWASI)}, + pages={184--188}, + year={2019}, + organization={IEEE} } -@article{burgholzer2021ec, - title={Advanced Equivalence Checking for Quantum Circuits}, - volume={40}, - ISSN={1937-4151}, - url={http://dx.doi.org/10.1109/TCAD.2020.3032630}, - DOI={10.1109/tcad.2020.3032630}, - number={9}, - journal={IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems}, - publisher={Institute of Electrical and Electronics Engineers (IEEE)}, - author={Burgholzer, Lukas and Wille, Robert}, +@inproceedings{tmhd2, + title={Analysis and protection of the two-metric helper data scheme}, + author={Tebelmann, Lars and K{\"u}hne, Ulrich and Danger, Jean-Luc and Pehl, Michael}, + booktitle={International Workshop on Constructive Side-Channel Analysis and Secure Design}, + pages={279--302}, year={2021}, - month=sep, - pages={1810–1824} + organization={Springer} +} + +@article{smhd, + title={Helper Data Schemes for Coded Modulation and Shaping in Physical Unclonable Functions}, + author={Fischer, Robert FH}, + journal={arXiv preprint arXiv:2402.18980}, + year={2024} +} + +@book{dekking2005modern, + title={A Modern Introduction to Probability and Statistics: Understanding why and how}, + author={Dekking, Frederik Michel}, + year={2005}, + publisher={Springer Science \& Business Media} } diff --git a/content/SMHD.typ b/content/SMHD.typ index 32c231d..15f175f 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -1,3 +1,174 @@ -= S-Metric Helper Data Method += S-Metric Helper Data Method -#figure(include("../graphics/quantizers/two-metric-enroll.typ")) +A metric based @hda generates helper data at PUF enrollment to provide more reliable results at the reconstruction stage. +Each of these metrics correspond to a quantizer with different bounds to lower the risk of bit or symbol errors during reconstruction. + +== Background + +=== Distribution Independency + +The publications for the Two-Metric approach @tmhd1 and @tmhd2, as well as the generalized S-Metric approach @smhd make the assumption, that the PUF readout is "zero-mean Gaussian distributed" @smhd. +We propose, that a Gaussian distributed input für S-Metric quantization is not required for the operation of this quantizing algorithm. +Instead, any distribution can be used for input values given, that a CDF exists for that distribution and its parameters are known. +As already mentioned in @tilde-domain, this transformation will result in uniformly distributed values, where equi-probable areas in the real domain correspond to equi-distant areas in the Tilde-Domain. +Contrary to @tmhd1, @tmhd2 and @smhd, which display relevant areas as equi-probable in a normal distribution, we will use equi-distant areas in a uniform distribution for better understandability. +It has to be mentioned, that instead of transforming all values of the PUF readout into the Tilde-Domain, we could also use an inverse CDF to transform the bounds of our evenly spaced areas into the real domain with (normal) distributed values, which can be assessed as remarkably less computationally complex. + +=== Two-Metric Helper Data Method + +The most simple form of a metric-based @hda is the Two-Metric Helper Data Method, since the quantization only yields symbols of 1-bit width and uses the lead amount of metrics possible. +Publications @tmhd1 and @tmhd2 find all the relevant bounds for the enrollment and reconstruction phases under the assumption that the PUF readout is Gaussian distributed. +Because this approach is static, meaning the parameters for symbol width and number of metrics always stays the same, it is easier to calculate the bounds for 8 equi-probable areas with a standard deviation of $sigma = 1$ first and then multiplying them with the estimated standard deviation of the PUF readout. +This is done by fining two bounds $a$ and $b$, that +$ integral_a^b f_X(x) \dx = 1/8 $ +This operation yields 9 bounds defining these areas $-\T1$, $-a$, $-\T2$, $0$, $\T2$, $a$, $\T1$ and $plus.minus infinity$ +During the enrollment phase, we will $plus.minus a$ as our quantizing bounds, retuning $0$ if the absolute values is smaller than $a$ and $1$ otherwise. +The corresponding metric is chosen based on the following conditions: + +$ M = cases( + \M1\, x < -a or 0 < x < a, + \M2\, -a < x or 1 < a < x +) $ + +@fig:tmhd_enroll shows the curve of a quantizer $cal(Q)$, that would be used during the Two-Metric enrollment phase. At this point, we will still assume, that our input value $x$ is zero-mean Gaussian distributed. + +#grid( + columns: (1fr, 1fr), + [#figure( + include("../graphics/quantizers/two-metric/enrollment.typ"), + caption: [Two-Metric enrollment]) ], + [#figure( + include("../graphics/quantizers/two-metric/reconstruction.typ"), + caption: [Two-Metric reconstruction]) ] +) + + +The metric will be stored publicly for every quantized bit as helper data. +As previously described, each of these metrics correspond to a different quantizer. +Now, we can use the generated helper data in the reconstruction phase and define a reconstructed bit based on the chosen metric as follows: + +$ #grid( + columns: (1fr, 1fr), + align: (center, center), + math.equation($\M1: k = cases(0\, x < \T1 or \T2 < x, 1\, -\T1 < x < \T2)$, block: true, numbering: none), + math.equation($\M2: k = cases(0\, x < -\T2 or \T1 < x, 1\, -\T2 < x < \T1)$, block: true, numbering: none) +) $ + +@fig:tmhd_reconstruct illustrates the basic idea behind the Two-Metric method. Using the helper data, we will move the bounds of the original quantizer one octile to each side, yielding two new quantizers. +The advantage of this method comes from moving the point of uncertainty away from our readout position. + +@fig:tmhd_example_enroll and @fig:tmhd_example_reconstruct illustrate an example enrollment and reconstruction process. +We would consider the marked point the value of the initial measurement and the marked range our margin of error due to inaccuracies in the measurement process. +If we now were to use the quantizer shown in @fig:tmhd_example_enroll during both the enrollment and the reconstruction phases, we would risk a bit error, because the margin of error overlaps with the lower quantization bound $-a$. +But since we generated helper data during enrollment as depicted in @fig:tmhd_enroll, we can make use of a different quantizer $cal(R)(1, 2, x)$ whose boundaries do not overlap with the error margin of the measurement. + +#grid( + columns: (1fr, 1fr), + [#figure( + include("../graphics/quantizers/two-metric/example_enroll.typ"), + caption: [Example enrollment]) ], + [#figure( + include("../graphics/quantizers/two-metric/example_reconstruct.typ"), + caption: [Example reconstruction]) ] +) +#pagebreak() + +=== S-Metric Helper Data Method + +Going on, the Two-Metric Helper Data Method can be generalized as shown in @smhd. +This generalization allows for higher order bit quantization and the use of more than two metrics. + +A key difference to the Two-Metric approach is the alignment of quantization areas. +Methods described in @tmhd1 and @tmhd2 use two bounds for 1-bit quantization, namely $plus.minus a$. +Contrary, the method introduced by @smhd would look more like a sign based quantizer if the configuration $cal(Q)(2, 1)$ is used, using only one quantization bound at $x=0$. +@fig:smhd_compar1 and @fig:smhd_compar2 illustrate this difference. + +#grid( + columns: (1fr, 1fr), + [#figure( + include("../graphics/quantizers/s-metric/s-metric-compar1.typ"), + caption: [Two-Metric enrollment] + )], + [#figure( + include("../graphics/quantizers/s-metric/s-metric-compar2.typ"), + caption: [S-Metric enrollment with 1-bit configuration] + )] +) + +The generalization consists of two components: + +- *Higher order bit quantization* \ + We can introduce more steps to our quantizer and use them to extract more than one bit out of our PUF readout. +- *Using more than two metrics* \ + Instead of splitting each quantizer steam into only two equi-probable parts, we can increase the number of metrics at the cost of generating more helper data. + +== Implementation + +We will now propose a specific implementation of the S-Metric Helper Data Method. \ +As shown in @sect:dist_independency, we can use a CDF to transform our random distributed variable $X$ into the Tilde-Domain: $tilde(X)$. +This allows us to use equi-distant bounds for the quantizer instead of equi-probable ones. + +From now on we will use the following syntax for quantizers that use the S-Metric Helper Data Method: +$ cal(Q)(s, m, tilde(x)) $ + +where s defines the number of metrics, m the number of bits and $tilde(x)$ a Tilde-Domain transformed PUF measurement. +#pagebreak() +=== Enrollment + +To enroll our PUF key, we will first need to define the quantizer for higher order bit quantization and helper data generation. +Because our PUF readout $tilde(x)$ can be interpreted as a realization of a uniformly distributed variable $tilde(X)$, we can define the width $Delta$ of our quantizer bins as follows: + +$ Delta = frac(1, 2^m) $ + +For example, if we were to extract a symbol with the width of 2 bits from our PUF readout, we would need to evenly space $2^2 = 4$ bins. Using equation @eq:delta, the step size for a 2-bit quantizer would result to: + +$ Delta' = lr(frac(1, 2^m) mid(|))_(m=2)= frac(1, 4) $ + +@fig:smhd_two_bit shows a plot of the resulting quantizer function that would yield symbols with two bits for one measurement $tilde(x)$. + +#figure( + include("../graphics/quantizers/two-bit-enroll.typ"), + caption: [2-bit quantizer] +) + +Right now, this quantizer wouldn't help us generating any helper data. +To achieve that, we will need to divide a symbol step - one, that returns the corresponding quantized symbol - into multiple sub-steps. +More specifically, we will define the amount of metrics we want to use with the parameter $s$. Using $s$, we can define the step size $Delta_s$ as the division of $Delta$ by $s$: + +$ Delta_s = frac(Delta, s) = frac(frac(1, 2^m), s) = frac(1, 2^m * s) $ + +After this definition, we need to make an adjustment to our previously defined quantizer function, because we cannot simply return the quantized value based on a quantizer with step size $Delta_s$. +That would just increase the amounts of bits we will extract out of one measurement. +Instead, we will need to return a tuple, consisting of the quantized symbol and the metric ascertained that we will save as helper data for later. + +Going on in our example, we could choose the amount of our metrics to be 2. According to @eq:delta_s, we would then half out step size: + +$ Delta'_s = lr(frac(Delta', s)mid(|))_(s=2) = frac(1, 4 * 2) = frac(1, 8) $ + + +This means, we can update out quantizer function with the new step size $Delta'_s = frac(1, 8)$ and redefining its output as a tuple consisting of bit value and helper data. + +We can visualize the quantizer that we will use during the enrollment phase of a 2-bit 2-metric configuration as depicted in @fig:smhd_2_2_en. + +#grid( + columns: (1fr, 1fr), +[#scale(x: 80%, y: 80%)[ +#figure( + include("../graphics/quantizers/s-metric/2_2_en.typ"), + caption: [2-bit 2-metric enrollment] +) ]], +[#scale(x: 80%, y: 80%)[ +#figure( +include("../graphics/quantizers/s-metric/3_2_en.typ"), +caption: [2-bit 3-metric enrollment] +) ]]) + +To better demonstrate the generalization to $s$-metrics, @fig:smhd_3_2_en shows a 2-bit quantizer that generates helper data based on three metrics instead of two. +In that sense, increasing the number of metrics will increase the number of sub-steps for each symbol. + +We can now perform the enrollment of a full PUF readout. +Each measurement will be quantized with out quantizer $cal(E)$, returning a tuple consisting of the quantized symbol and helper data, as shown in @eq:smhd_quant + +$ K_i = cal(E)(s, m tilde(x_i)) = (k, h)_i $ + +Performing the operation of @eq:smhd_quant for our whole set of measurements will yield a vector of tuples $bold(K)$. diff --git a/content/introduction.typ b/content/introduction.typ index 236caeb..42b59e3 100644 --- a/content/introduction.typ +++ b/content/introduction.typ @@ -13,11 +13,14 @@ Vectors will be written in bold test: $bold(k)$ represents a vector of quantized We will call a quantized symbol $k$. $k$ consists of all possible binary symbols, i.e. $0, 01, 110$. A quantizer will be defined as a function $cal(Q)(x, bold(a))$ that returns a quantized symbol $k$. +We also define the following special quantizers for metric based HDAs: +A quantizer used during the enrollment phase is defined by a calligraphic $cal(E)$. +For the reconstruction phase, a quantizer will be defined by a calligraphic $cal(R)$ @example-quantizer shows the curve of a 2-bit quantizer that receives $tilde(x)$ as input. In the case, that the value of $tilde(x)$ equals one of the four bounds, the quantized value is chosen randomly from the relevant bins. #figure( - include("../graphics/quantizers/two-metric-enroll.typ"), + include("../graphics/quantizers/two-bit-enroll.typ"), caption: [Example quantizer function]) For the S-Metric Helper Data Method, we introduce a function @@ -28,8 +31,12 @@ where s determines the amount of metrics and m the bit width of the symbols. === Tilde-Domain -AS also described in REFSMHD, we will use a CDF to transform the real PUF values into the Tilde-Domain -This transformation can be performed using the function $sym(xi) = tilde(x)$. The key property of this transformation is the resulting uniform distribution of $x$. +AS also described in @smhd, we will use a CDF to transform the real PUF values into the Tilde-Domain +This transformation can be performed using the function $xi = tilde(x)$. The key property of this transformation is the resulting uniform distribution of $x$. Considering a normal distribution, the CDF is defined as -$ sym(xi)(frac(x - sym(mu))(sym(sigma))) = frac(1)(2)[1 + erf(frac(x - sym(mu))(sym(sigma) sqrt(2)))] $ +$ xi(frac(x - mu, sigma)) = frac(1, 2)[1 + \e\rf(frac(x - mu, sigma sqrt(2)))] $ + +=== ECDF + +The eCDF is constructed through sorting the empirical measurements of a distribution @dekking2005modern. Although less accurate, this method allows a more simple and less computationally complex way to transform real valued measurements into the Tilde-Domain. We will mainly use the eCDF in @chap:smhd because of the difficulty of finding an analytical description for the CDF of a Gaussian-Mixture. diff --git a/glossary.typ b/glossary.typ index 4799995..117a8eb 100644 --- a/glossary.typ +++ b/glossary.typ @@ -4,6 +4,7 @@ #heading(numbering: none)[Glossary] #print-glossary(( + (key: "hda", short: "HDA", plural: "HDAs", long: "helpder data algorithm", longplural: "helper data algorithms"), (key: "bdd", short: "BDD", plural: "BDDs", long: "binary decision diagram", longplural: "binary decision diagrams"), (key: "dd", short: "DD", plural: "DDs", long: "decision diagram", longplural: "decision diagrams"), (key: "mqt", short: "MQT", long: "Munich Quantum Toolkit"), diff --git a/graphics/quantizers/s-metric/2_2_en.typ b/graphics/quantizers/s-metric/2_2_en.typ new file mode 100644 index 0000000..cf7bfdd --- /dev/null +++ b/graphics/quantizers/s-metric/2_2_en.typ @@ -0,0 +1,30 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw, decorations, vector + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#canvas({ + plot.plot(size: (8,6), + x-tick-step: 0.25, + y-label: $cal(E)(2, 2, tilde(x))$, + x-label: $tilde(x)$, + y-tick-step: none, + y-ticks: ((0.125, [M1]) ,(0.25, [M2]),(0.375, [M1]) ,(0.5, [M2]),(0.625, [M1]) ,(0.75, [M2]),(0.875, [M1]) ,(1, [M2])), + axis-style: "left", + x-min: 0, + x-max: 1, + y-min: 0, + y-max: 1,{ + plot.add(((0,0), (0.125, 0.125), (0.25,0.25), (0.375, 0.375),(0.5,0.5), (0.625, 0.625),(0.75,0.75), (0.875, 0.875),(1, 1)), line: "vh", style: line_style) + plot.add-hline(0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1, style: dashed) + plot.add-vline(0.25, 0.5, 0.75, 1, style: dashed) + }) + decorations.brace((-0.9,0.63), (-0.9,1.63), name: "00") + decorations.brace((-0.9,2.13), (-0.9,3.13), name: "01") + decorations.brace((-0.9,3.63), (-0.9,4.63), name: "10") + decorations.brace((-0.9,5.13), (-0.9,6.13), name: "11") + + draw.content((v => vector.add(v, (-0.3, 0)), "00.west"), [00]) + draw.content((v => vector.add(v, (-0.3, 0)), "01.west"), [01]) + draw.content((v => vector.add(v, (-0.3, 0)), "10.west"), [10]) + draw.content((v => vector.add(v, (-0.3, 0)), "11.west"), [11]) +}) diff --git a/graphics/quantizers/s-metric/3_2_en.typ b/graphics/quantizers/s-metric/3_2_en.typ new file mode 100644 index 0000000..13d6bb7 --- /dev/null +++ b/graphics/quantizers/s-metric/3_2_en.typ @@ -0,0 +1,30 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw, decorations, vector + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#canvas({ + plot.plot(size: (8,6), + x-tick-step: 0.25, + y-label: $cal(E)(3, 2, tilde(x))$, + x-label: $tilde(x)$, + y-tick-step: none, + y-ticks: ((1/12, [M1]) ,(2/12, [M2]),(3/12, [M3]) ,(4/12, [M1]),(5/12, [M2]) ,(6/12, [M3]),(7/12, [M1]) ,(8/12, [M2]), (9/12, [M3]), (10/12, [M1]), (11/12, [M2]), (1, [M3])), + axis-style: "left", + x-min: 0, + x-max: 1, + y-min: 0, + y-max: 1,{ + plot.add(((0,0), (1/12, 1/12), (2/12,2/12), (3/12, 3/12),(4/12,4/12), (5/12, 5/12),(6/12,6/12), (7/12, 7/12),(8/12, 8/12), (9/12, 9/12), (10/12, 10/12), (11/12, 11/12), (1, 1)), line: "vh", style: line_style) + plot.add-hline(1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 1, style: dashed) + plot.add-vline(0.25, 0.5, 0.75, 1, style: dashed) + }) + decorations.brace((-0.9,0.4), (-0.9,1.63), name: "00") + decorations.brace((-0.9,1.9), (-0.9,3.13), name: "01") + decorations.brace((-0.9,3.4), (-0.9,4.63), name: "10") + decorations.brace((-0.9,4.9), (-0.9,6.13), name: "11") + + draw.content((v => vector.add(v, (-0.3, 0)), "00.west"), [00]) + draw.content((v => vector.add(v, (-0.3, 0)), "01.west"), [01]) + draw.content((v => vector.add(v, (-0.3, 0)), "10.west"), [10]) + draw.content((v => vector.add(v, (-0.3, 0)), "11.west"), [11]) +}) diff --git a/graphics/quantizers/s-metric/s-metric-compar1.typ b/graphics/quantizers/s-metric/s-metric-compar1.typ new file mode 100644 index 0000000..00917a3 --- /dev/null +++ b/graphics/quantizers/s-metric/s-metric-compar1.typ @@ -0,0 +1,25 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: teal) +#let fill_olive = (stroke: none, fill: maroon) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: ((-1.25, [-a]), (1.25, [a]), (0, [0])), + y-label: $cal(E)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (-1.25,0), (-1.25,1), (1.25,1), (1.25, 0), (3, 0)), line: "vh", style: line_style) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/graphics/quantizers/s-metric/s-metric-compar2.typ b/graphics/quantizers/s-metric/s-metric-compar2.typ new file mode 100644 index 0000000..6d65948 --- /dev/null +++ b/graphics/quantizers/s-metric/s-metric-compar2.typ @@ -0,0 +1,25 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: teal) +#let fill_olive = (stroke: none, fill: maroon) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: (0, 0), + y-label: $cal(E)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (0,0), (0,1), (3,1)), line: "vh", style: line_style) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/graphics/quantizers/two-metric-enroll.typ b/graphics/quantizers/two-bit-enroll.typ similarity index 100% rename from graphics/quantizers/two-metric-enroll.typ rename to graphics/quantizers/two-bit-enroll.typ diff --git a/graphics/quantizers/two-metric/enrollment.typ b/graphics/quantizers/two-metric/enrollment.typ new file mode 100644 index 0000000..b14a64d --- /dev/null +++ b/graphics/quantizers/two-metric/enrollment.typ @@ -0,0 +1,30 @@ +#import "@preview/cetz:0.2.2": canvas, plot + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: teal) +#let fill_olive = (stroke: none, fill: maroon) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: ((-1.25, [-a]), (1.25, [a]), (0, [0])), + y-label: $cal(E)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (-1.25,0), (-1.25,1), (1.25,1), (1.25, 0), (3, 0)), line: "vh", style: line_style) + plot.add-fill-between(((-3, 0), (-1.25, 0)), ((-3, 1), (-1.25, 1)), style: fill_aqua, label: [Use metric 1]) + plot.add-fill-between(((-1.25, 0), (0, 0)), ((-1.25, 1), (0, 1)), style: fill_olive, + label: [Use metric 2]) + plot.add-fill-between(((0, 0), (1.25, 0)), ((0, 1), (1.25, 1)), style: fill_aqua) + plot.add-fill-between(((1.25, 0), (3, 0)), ((1.25, 1), (3, 1)), style: fill_olive) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/graphics/quantizers/two-metric/example_enroll.typ b/graphics/quantizers/two-metric/example_enroll.typ new file mode 100644 index 0000000..a8826b5 --- /dev/null +++ b/graphics/quantizers/two-metric/example_enroll.typ @@ -0,0 +1,27 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: teal) +#let fill_olive = (stroke: none, fill: maroon) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: ((-1.25, [-a]), (1.25, [a]), (0, [0])), + y-label: $cal(E)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (-1.25,0), (-1.25,1), (1.25,1), (1.25, 0), (3, 0)), line: "vh", style: line_style) + plot.add(((-1.8, 0), (-1.1, 0)), mark: "|", mark-size: .4, mark-style: (stroke: (thickness: 2pt, paint: blue)), style: (stroke: (paint: blue, thickness: 2pt))) + plot.add(((-1.45, 0), (-1.45, 0)), mark: "o", mark-style: (stroke: (paint: red), fill: red)) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/graphics/quantizers/two-metric/example_reconstruct.typ b/graphics/quantizers/two-metric/example_reconstruct.typ new file mode 100644 index 0000000..a35e455 --- /dev/null +++ b/graphics/quantizers/two-metric/example_reconstruct.typ @@ -0,0 +1,27 @@ +#import "@preview/cetz:0.2.2": canvas, plot, draw + +#let line_style = (stroke: (paint: black, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: teal) +#let fill_olive = (stroke: none, fill: maroon) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: ((-1.25, [-a]), (1.25, [a]), (0, [0])), + y-label: $cal(R)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (-2.125,0), (-2.125,1), (0.375,1), (0.375, 0), (3, 0)), line: "vh", style: line_style) + plot.add(((-1.8, 0), (-1.1, 0)), mark: "|", mark-size: .4, mark-style: (stroke: (thickness: 2pt, paint: blue)), style: (stroke: (paint: blue, thickness: 2pt))) + plot.add(((-1.45, 0), (-1.45, 0)), mark: "o", mark-style: (stroke: (paint: red), fill: red)) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/graphics/quantizers/two-metric/reconstruction.typ b/graphics/quantizers/two-metric/reconstruction.typ new file mode 100644 index 0000000..925d8bd --- /dev/null +++ b/graphics/quantizers/two-metric/reconstruction.typ @@ -0,0 +1,28 @@ +#import "@preview/cetz:0.2.2": canvas, plot + +#let line_style_aqua = (stroke: (paint: teal, thickness: 2pt)) +#let line_style_eastern = (stroke: (paint: maroon, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#let fill_aqua = (stroke: none, fill: aqua) +#let fill_olive = (stroke: none, fill: eastern) +#canvas({ + plot.plot(size: (7,3), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: none, + x-ticks: ((-1.25, [-a]), (1.25, [a]), (0, [0]), (-2.125, [-T1]), (2.125, [T1]), (0.375, [T2]), (-0.375, [-T2])), + y-label: $cal(R)(1, 2, x)$, + x-label: $x$, + y-tick-step: none, + y-ticks: ((0, [0]), (1, [1])), + axis-style: "left", + x-min: -3, + x-max: 3, + y-min: 0, + y-max: 1,{ + plot.add(((-3,0), (-2.125,0), (-2.125,1), (0.375,1), (0.375, 0), (3, 0)), line: "vh", style: line_style_aqua, label: [Metric 1]) + plot.add(((-3, 0), (-0.375, 0), (-0.375, 1), (2.125, 1), (2.125, 0), (3, 0)), line: "vh", style: line_style_eastern, label: [Metric 2]) + //plot.add-fill-between(((1.25, 0), (3, 0)), ((1.25, 1), (3, 1)), style: fill_olive) + plot.add-hline(1, style: dashed) + }) +}) diff --git a/main.pdf b/main.pdf index 02e8fbc551df61daf2f2fd353f6136b135e1b825..91bd268ec70b0bb6ce2fbce1fa41ca3fbc847044 100644 GIT binary patch delta 176817 zcmbRBO!oI7IU&^m7dKr)J##MAhK7a)E-pjM$rER*OuxB?Nti7>!acy-XQIEgtbu}o zLQpK1f`WcXerR51a(+sxf{_tOkju_)x?>2t-1N+~OxiFV->Ml6r;D#+vf;5*uv9QN zFwrx$u(X(blF?btQo+bV!Nkl&&%(sm+*HBH5{!&Z^(>4nElehRFrDNxR4_GEFf}pI zGc__dHkoYC96xy-b0?pfKC8Bhp@NZ#fuVw-fr+`Eg{h&Lf|04A34|~PQk{&z{qTJKBv!Qqqw@s?p)H7_r}#t{=;QCIW3-Va#Or3r?Degm8tpU-P|o4 zE?|zC<79_~CzEA)`M3<6T){$a&Xd)7ZMe)_E$kF*j0}v7Cdcz?Ng0CWOic_7%q;A< zYz!=2jKCshW|NomDowu5TRB;hjSu8J7Em}$Z**Z-seikdyC&r7R{MS5Ez{4JnM$>OIkWZMj28 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#include "glossary.typ"