From 8dbb73a8cfdfb6e039855f9575a11ae874e54e04 Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Fri, 19 Jul 2024 20:54:01 +0200 Subject: [PATCH] Continued on Reconstruction --- content/SMHD.typ | 13 +++++++-- .../s-metric/2_2_found_quantizer1.typ | 2 +- .../s-metric/2_2_reconstruction.typ | 26 ++++++++++++++++++ main.pdf | Bin 538053 -> 541417 bytes 4 files changed, 38 insertions(+), 3 deletions(-) create mode 100644 graphics/quantizers/s-metric/2_2_reconstruction.typ diff --git a/content/SMHD.typ b/content/SMHD.typ index 20ffdc5..81082e8 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -190,7 +190,7 @@ If $s$ is even, we need to move our quantizer $s/2$ times some distance to the r We can define the ideal position for the quantizer bounds based on its corresponding metric as centered around the center of the related metric. We can find these new bounds graphically as depicted in @fig:smhd_find_bound_graph. We first determine the x-values of the centers of a metric (here M1, as shown with the arrows). We can then place the quantizer steps with step size $Delta$ (@eq:delta) evenly spaced around these points. - +With these new points for the vertical steps of $cal(Q)$, we can draw the new quantizer for the first metric in @fig:smhd_found_bound_graph. #grid( @@ -205,5 +205,14 @@ We can find these new bounds graphically as depicted in @fig:smhd_find_bound_gra #figure( include("../graphics/quantizers/s-metric/2_2_found_quantizer1.typ"), caption: [Quantizer for the first metric] - )]] + )]] ) + +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 $cal(R)(2,2,tilde(x))$. + +#figure( + include("../graphics/quantizers/s-metric/2_2_reconstruction.typ"), + caption: [2-bit 2-metric reconstruction quantizer] +) + + diff --git a/graphics/quantizers/s-metric/2_2_found_quantizer1.typ b/graphics/quantizers/s-metric/2_2_found_quantizer1.typ index 9c8e469..ddb97ed 100644 --- a/graphics/quantizers/s-metric/2_2_found_quantizer1.typ +++ b/graphics/quantizers/s-metric/2_2_found_quantizer1.typ @@ -6,7 +6,7 @@ plot.plot(size: (8,6), x-tick-step: none, x-ticks: ((3/16, [3/16]), (7/16, [7/16]), (11/16, [11/16]), (15/16, [15/16])), - y-label: $cal(Q)(2, 1, tilde(x))$, + y-label: $cal(Q)(2, 2, tilde(x))$, x-label: $tilde(x)$, y-tick-step: none, y-ticks: ((3/16, [00]), (7/16, [01]), (11/16, [10]), (15/16, [11])), diff --git a/graphics/quantizers/s-metric/2_2_reconstruction.typ b/graphics/quantizers/s-metric/2_2_reconstruction.typ new file mode 100644 index 0000000..a66f6f1 --- /dev/null +++ b/graphics/quantizers/s-metric/2_2_reconstruction.typ @@ -0,0 +1,26 @@ +#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 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: $cal(R)(2, 2, tilde(x))$, + x-label: $tilde(x)$, + y-tick-step: none, + y-ticks: ((3/16, [00]), (7/16, [01]), (11/16, [10]), (15/16, [11])), + 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) + }) +}) diff --git a/main.pdf b/main.pdf index 8d3ee5ce5faab69b9053ac49089213dddd90a888..1e0e0a2d9a070c7856fc9847c3d0ed2b1d8f3d77 100644 GIT binary patch delta 163517 zcmX^5TH$4@qM&Mki<_>Yo;jClLqkIY7njlG#%Ze4_h~Q-PyC}iF-J?vNWnlMD3(h> zK|drvG%qtbKP6Sc$OI%fxrAAD>IP=s=?R+5QWO95G8#{3bY?c3oDjgX`8eY)Mn>c5 zi8}1UlP~zOOpXhZn7omBEr%&cBbS}sSXUCPAmy(~91qzCb-^4e21-CMZS=cGq7#J9v*>Twz7#LbYc;=g* zhTdSB{9r2o^#5uc94w~BmS)p8zGqjhujQxq^rOoceIFBk|O!nh1_=#;<>sgBJ_y zMjuxG@Yi6Aq}128Vd2o$mFPocH4elTPpN`?+`D{P?))kPh4X zEx-BWvQU9j)f%NwEf{&KjDf-M5zIS_> zPrurH(MJLglzTkix7^>HbNBRz+8B=O$5tj-B%Sp7w?jbQiv4YDu;Txas9)iB%13JJ 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