From bec072211160c624cb5b4d0f1e1e32819d3e6ef0 Mon Sep 17 00:00:00 2001 From: Marius Drechsler Date: Sun, 21 Jul 2024 17:19:09 +0200 Subject: [PATCH] Yes --- content/SMHD.typ | 23 +++++++++++++++--- .../s-metric/2_2_found_quantizer1.typ | 6 ++--- .../s-metric/2_2_reconstruction.typ | 4 +-- .../s-metric/3_2_reconstruction.typ | 4 +-- main.pdf | Bin 546943 -> 550256 bytes pseudocode/find_quantizers.typ | 18 +++++--------- 6 files changed, 33 insertions(+), 22 deletions(-) diff --git a/content/SMHD.typ b/content/SMHD.typ index 1b56a77..d58fe2b 100644 --- a/content/SMHD.typ +++ b/content/SMHD.typ @@ -230,14 +230,31 @@ As for metric 2, we can apply the same strategy and find the points for the vert 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 $ +$ phi = lr(frac(1, 2^n dot s dot 2)mid(|))_(n=2, s=2) = 1 / 16 $ -This is also shown in @fig:smhd_2_2_reconstruction, as our quantizer curve is moved $1/8$ to the left and the right. +This is also shown in @fig:smhd_2_2_reconstruction, as our quantizer curve is moved $1/16$ 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. +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 (@fig:smhd_3_2_reconstruction). +Comparing @fig:smhd_2_2_reconstruction, @fig:smhd_3_2_reconstruction and their respective values of @eq:offset, we can observe, that the offset $phi$ gets smaller the more metrics we use. +] + + +#figure( + table( + columns: (11), + inset: 7pt, + align: center + horizon, + [$m$], + [1],[2],[3],[4],[5],[6],[7],[8],[9],[10], + [$phi$],[$1/8$],table.cell(fill: gray)[$1/16$], [$1/24$], table.cell(fill:gray)[$1/32$], [$1/40$], table.cell(fill:gray)[$1/48$], [$1/56$], table.cell(fill:gray)[$1/64$], [$1/72$], table.cell(fill:gray)[$1/80$] + ), + caption: [Offset values for 2-bit configurations] +) + +Before we can go deeper into the properties of the offset value $phi$, we will introduce a way to programmatically find the offset values for all s quantizers. #figure( kind: "algorithm", supplement: [Algorithm], diff --git a/graphics/quantizers/s-metric/2_2_found_quantizer1.typ b/graphics/quantizers/s-metric/2_2_found_quantizer1.typ index ddb97ed..5cd8759 100644 --- a/graphics/quantizers/s-metric/2_2_found_quantizer1.typ +++ b/graphics/quantizers/s-metric/2_2_found_quantizer1.typ @@ -9,14 +9,14 @@ 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])), + y-ticks: ((1/4, [00]), (2/4, [01]), (3/4, [10]), (4/4, [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) - plot.add-hline(3/16, 7/16, 11/16, 15/16, style: dashed) + plot.add(((0,1/4), (3/16,1/4), (7/16,2/4), (11/16,3/4), (15/16, 4/4), (15/16, 1/4), (1, 1/4)), line: "vh", style: line_style) + plot.add-hline(1/4, 2/4, 3/4, 1, style: dashed) plot.add-vline(3/16, 7/16, 11/16, 15/16, style: dashed) }) }) diff --git a/graphics/quantizers/s-metric/2_2_reconstruction.typ b/graphics/quantizers/s-metric/2_2_reconstruction.typ index d3a7b53..fb9940d 100644 --- a/graphics/quantizers/s-metric/2_2_reconstruction.typ +++ b/graphics/quantizers/s-metric/2_2_reconstruction.typ @@ -18,8 +18,8 @@ x-max: 1, y-min: 0, y-max: 1,{ - 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(((0,1/4), (3/16,1/4), (7/16,2/4), (11/16,3/4), (15/16, 1), (15/16, 1/4), (1, 1/4)), line: "vh", style: line_style, label: [Metric 1]) + plot.add(((0, 1), (1/16, 1), (1/16, 1/4), (5/16, 1/4), (9/16, 2/4), (13/16, 3/4), (13/16, 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 index 449123f..ce288d5 100644 --- a/graphics/quantizers/s-metric/3_2_reconstruction.typ +++ b/graphics/quantizers/s-metric/3_2_reconstruction.typ @@ -19,9 +19,9 @@ 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), (5/24, 1/4), (11/24, 2/4), (17/24, 3/4), (23/24, 1), (23/24, 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, 1/4), (4/12, 1/4), (4/12, 2/4), (7/12, 3/4), (10/12, 1), (1, 1)), line: "hv", style: line_style3, label: [Metric 3]) + plot.add(((0, 1),(1/24, 1), (1/24, 1/4), (7/24, 1/4), (7/24, 2/4), (13/24, 3/4), (19/24, 1), (1, 1)), line: "hv", style: line_style3, label: [Metric 3]) 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/main.pdf b/main.pdf index a54db616d90d13120086418a0ce40d770952a69e..656a2cd690c655004280821217569c84250d561f 100644 GIT binary patch delta 138211 zcmeyrLGi;WMM2d77dKr)J##MAhK7a)E-s_#iEPZO(;Ez!g(v<|o|vO0WvpPJ5ERR$ zpr9X;ADWk$oS%}aU}OpsoLtAOIyvSI@8k!8QWO95GMY?3V90E^c{k$)#>rJIeACad zGILFi|0pqeH}hH!Gms80JG;sEITbcfV2Na9G@Gu-#VoSb)ygex= zl8JLdi?5IfgV(Z4DrL&IJLjCRoO`4%=lIS!i?daIVRG{*Q?F%w zH|IW9^DUnn@nqlkG&w#wyIWsw-(Ao4MVR0C^Z7lM-}lUv7n&uY?AEWJmHAnsU*CVid{!E@9f9&^f`?y4)UB30#I!}!a zSC;Y|`u_Yu_1h;UU$&Xs&iZDj*tdjZVw91n)aSpS_ujW>UJ=5PSbu8fx4UN9RR&+1 z1d`8QxHsdYFZ-UCv-dIIXSDx*?Ph>VmZaZbW5s)488hC`<7H1X-n{P%r{cZer5XRd z7iQNluMeEz+Eo|U9@+W!Q}FJ{Et#=SFJ@+HTI~zU6MwYv?x7oMSF(>^i&Z`(aC86l zugk^fiN~AQM%!?!R4}|Q+5FF>{)!}10h`vP)GEh}l4RBzW{>kiD{pasu#NuXc6HAs z?{@28hU+1Tf|(ANc_wOZdhkzXqV^{jy9+n9xLhY{h?xZ{dAZKiXuqiCI&}qG%$r4S z7A|X72>U%0`nt%`q)Y9hPE<>DMN9aWF0+ezRxZn52;E)e{-w+AqCVRZDMO96BlS^+ zI@dbCCNRKF;{R{b>79_an!T%<412F)%!j=`$$(w=bo-!_vS}_g+Y6Q=Unvb za6j^VtK>&M-8HU9WFN)e+97sD&2+w)PLV*YbT6m~ zsEL^)K3||-UUa_5e4+Vb{awe8u)fuOw7>KC(fOVF8J0;wXF9959KI#^*6m~5+ZAP# z%bGnd)^UZ*V2PU5`0u8{bl0_>udi*(s@_t2%kaRrDc{uI-mThsZ|(o7|9Jnp|LXUB zZ(4ili|gfJw}pXeA(EzTmp@3=9%FlKT()}ev3FZ`XMdS>W!9bgSxvJR&Du0;)vRT+ zbWM+EGnM-PSNUD9|1T~+MupS($l+NR?nJHM=6rkg+v|PVi*Mx`1abC!F_n19{_E-u zkFdo@Rv7R|tt@Yy_$hJ8r5he~5}pS+f|Mk9S z`=9MD`*CYwHv9UwySM$m)t3GB`lt0z|GWqeEzV32y1&UMyiX8y_WsO z^$Cpa2Va$T6en=@HJH9^2vYnczP(dMH-1U>?*rX;_~yq8vhIouX_zkfKs1YGhTX+I ze;0Y&uYIw3R@u7`uDKu2btgGL6;8P5dps|1r^c4F!#5=E6gXP*#eYfD$k@W1l4WKV zYj8F9R`rR(8y4Af?!L0m&M{J}{l~3Y`h`=padUmU?J?Gk?*jz>y|Yi*zu{X!B@d5` z-5vJ7OA_ogubjVm_`+e`RqfF$*k3%bGBGmGH`kjnXE*;_%aVuRc%O=2%d?2d+b%7w zZ?pCHh1TU}Q*QIiw}q`V^m+KX_n=VgX4V3~Towi2Z=3jkHR$opx7FTn`9^%6RrR(% zI%k|~_pj(&TF;st%IG6wZE!Vr&x*VIX0OUCzj1owfyD9~jB5`|C#?AL?Co#9T$Uqm z+M_!*t9_VgRpBuq>eFl{*%kkE8&)@P`+Yo<`r`yk`HV{?l6O+o_6V+OJ)hOkcJ_h1 z@j>=9uD?e%$j+F|sb?yDCrxd~F`t6^nGYTr9h6LI;z;e%s-K%VpcDy=u@bIbyV%%A- z-yS?X{or2k!H3ID650J3maWu3$jczfP#L}3`gXTXlzaI11=nsqEV;5IDyBKAI=V10 zah0mO_NJ$|Kb!9Ow{Cf`{$}ZVR^6*tbywz2%Z;5o+k0+lq`%&et@*kgJHNhu{%N=M zo2zBnx!J|lx1NO3&Bqh;mNB*#@JWNqH$US&9ZC~5X#-W~j}?#^1ieDmVxPaf1S zv#FjP`~RY@{e0`M-7h=m&wW#Q_~i!in=5tqaoqa0-sGR}^u!!)BPq9|hQXYtSUnWX zbyvhXR0|tiQ1Nls@8Vfd|1Wf6kGqUvtEOU_V%Dx(s~Pso+)WCsczQefZU6mGn|B8P zH?aL!?2v8uh;dd)SNefZ@0tQPDY`LE=1H1fbn zelLvut7=rC_FyHO$IN7pmmST0HSJB>2kw4TI)32i=kNFXzdNg}+AF%otBu36E1R># z@3{44*PoYOPT*L2!edkB4V86{%5OCo^4%V=F!&o896FGEC#{1afA!so?_cP!@omk{ zw=G|om+T)~|BCZ%_V%os-_}(<;^tU+AvfXetF1G;7hNotj9K{Pa4JWjuE2sz5Bd|M z-&o9V6nG)i>&Y7pYgX*&OU*tfswdwOetE z=i(-&Pe0jKvy>S;aDKq@Fl}id*ZKob8=J%&=FgIGe!x;1bLMk>fP>|cdr~JQw3a

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