From b73f8e6e63247c7e9f9dd07aebba1c33313891f9 Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Sat, 20 Jul 2024 20:09:02 +0200 Subject: [PATCH] More reconstruction --- content/SMHD.typ | 36 ++++++++++++++++-- .../s-metric/2_2_reconstruction.typ | 10 ++--- .../s-metric/3_2_reconstruction.typ | 28 ++++++++++++++ main.pdf | Bin 541417 -> 546943 bytes pseudocode/find_quantizers.typ | 16 ++++++++ 5 files changed, 82 insertions(+), 8 deletions(-) create mode 100644 graphics/quantizers/s-metric/3_2_reconstruction.typ create mode 100644 pseudocode/find_quantizers.typ diff --git a/content/SMHD.typ b/content/SMHD.typ index 81082e8..1b56a77 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -210,9 +210,39 @@ With these new points for the vertical steps of $cal(Q)$, we can draw the new qu As for metric 2, we can apply the same strategy and find the points for the vertical steps to be at $1/16, 5/16, 9/16$ and $13/16$. This quantizer can be visualized together with the first metric quantizer in @fig:smhd_2_2_reconstruction, forming the complete quantizer for the reconstruction phase of a 2-bit 2-metric configuration $cal(R)(2,2,tilde(x))$. +#grid( + columns: (1fr, 1fr), + [ + #scale(x: 80%, y: 80%)[ + #figure( + include("../graphics/quantizers/s-metric/2_2_reconstruction.typ"), + caption: [2-bit 2-metric reconstruction quantizer] + ) ] + ], + [ + #scale(x: 80%, y: 80%)[ + #figure( + include("../graphics/quantizers/s-metric/3_2_reconstruction.typ"), + caption: [2-bit 3-metric reconstruction quantizer], + ) ] + ] +) + +Analytically, the offset we are applying to $cal(E)(2, 2, tilde(x))$ can be defined as + +$ phi = lr(frac(1, 2^n dot s)mid(|))_(n=2, s=2) = 1 / 8 $ + +This is also shown in @fig:smhd_2_2_reconstruction, as our quantizer curve is moved $1/8$ to the left and the right. + +==== Odd number of metrics + +If a odd number of metrics is given, the offset can still be calculated using @eq:offset. Additionally, we will keep the original quantizer used during enrollment. + #figure( - include("../graphics/quantizers/s-metric/2_2_reconstruction.typ"), - caption: [2-bit 2-metric reconstruction quantizer] -) + kind: "algorithm", + supplement: [Algorithm], + include("../pseudocode/find_quantizers.typ") +) +As shown in @alg:fancy diff --git a/graphics/quantizers/s-metric/2_2_reconstruction.typ b/graphics/quantizers/s-metric/2_2_reconstruction.typ index a66f6f1..d3a7b53 100644 --- a/graphics/quantizers/s-metric/2_2_reconstruction.typ +++ b/graphics/quantizers/s-metric/2_2_reconstruction.typ @@ -12,15 +12,15 @@ y-label: $cal(R)(2, 2, tilde(x))$, x-label: $tilde(x)$, y-tick-step: none, - y-ticks: ((3/16, [00]), (7/16, [01]), (11/16, [10]), (15/16, [11])), + y-ticks: ((1/4, [00]), (2/4, [01]), (3/4, [10]), (1, [11])), axis-style: "left", x-min: 0, x-max: 1, y-min: 0, y-max: 1,{ - plot.add(((0,3/16), (3/16,3/16), (7/16,7/16), (11/16,11/16), (15/16, 15/16), (15/16, 3/16), (1, 3/16)), line: "vh", style: line_style, label: [Metric 1]) - plot.add(((0, 15/16), (1/16, 15/16), (1/16, 3/16), (5/16, 3/16), (9/16, 7/16), (13/16, 11/16), (13/16, 15/16), (1, 15/16)),line: "vh", style: line_style2, label: [Metric 2]) - plot.add-hline(3/16, 7/16, 11/16, 15/16, style: dashed) - plot.add-vline(3/16, 7/16, 11/16, 15/16, style: dashed) + plot.add(((0,1/4), (1/8,1/4), (3/8,2/4), (5/8,3/4), (7/8, 1), (7/8, 1/4), (1, 1/4)), line: "vh", style: line_style, label: [Metric 1]) + plot.add(((0, 1), (1/8, 1), (1/8, 1/4), (3/8, 1/4), (5/8, 2/4), (7/8, 3/4), (7/8, 1), (1, 1)),line: "vh", style: line_style2, label: [Metric 2]) + plot.add-hline(1/4, 2/4, 3/4, 1, style: dashed) + plot.add-vline(1/4, 2/4, 3/4, 1, style: dashed) }) }) diff --git a/graphics/quantizers/s-metric/3_2_reconstruction.typ b/graphics/quantizers/s-metric/3_2_reconstruction.typ new file mode 100644 index 0000000..449123f --- /dev/null +++ b/graphics/quantizers/s-metric/3_2_reconstruction.typ @@ -0,0 +1,28 @@ +#import "@preview/cetz:0.2.2": canvas, plot + +#let line_style = (stroke: (paint: red, thickness: 2pt)) +#let line_style2 = (stroke: (paint: blue, thickness: 2pt)) +#let line_style3 = (stroke: (paint: green, thickness: 2pt)) +#let dashed = (stroke: (dash: "dashed")) +#canvas({ + plot.plot(size: (8,6), + legend: "legend.south", + legend-style: (orientation: ltr, item: (spacing: 0.5)), + x-tick-step: 1/4, + //x-ticks: ((3/16, [3/16]), (7/16, [7/16]), (11/16, [11/16]), (15/16, [15/16])), + y-label: $cal(R)(3, 2, tilde(x))$, + x-label: $tilde(x)$, + y-tick-step: none, + y-ticks: ((1/4, [00]), (2/4, [01]), (3/4, [10]), (1, [11])), + axis-style: "left", + x-min: 0, + x-max: 1, + y-min: 0, + y-max: 1,{ + plot.add(((0, 1/4), (2/12, 1/4), (5/12, 2/4), (8/12, 3/4), (11/12, 1), (11/12, 1/4), (1, 1/4)),line: "vh", style: line_style, label: [Metric 1]) + plot.add(((0,1/4), (1/4,1/4), (2/4,2/4), (3/4,3/4), (4/4, 4/4)), line: "vh", style: line_style2, label: [Metric 2]) + plot.add(((0, 1),(1/12, 1), (1/12, 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