Move figures to next chapter
This commit is contained in:
@@ -45,8 +45,8 @@
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\centering
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% tex-fmt: off
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\begin{quantikz}[row sep=4mm, column sep=4mm]
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& \xyzerr & \ctrl{3} & & & & & \\
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\lstick{$\ket{\psi}$} & \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\
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\lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & & & & & \\
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& \xyzerr & & \ctrl{2} & \ctrl{3} & & & \\
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& \xyzerr & & & & \ctrl{2} & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \meter{} & \setwiretype{c}
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@@ -59,8 +59,8 @@
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\centering
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% tex-fmt: off
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\begin{quantikz}[row sep=4mm, column sep=4mm]
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& \xerr & \ctrl{3} & & & & & & \\
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\lstick{$\ket{\psi}$} & \xerr & & \ctrl{2} & \ctrl{3} & & & & \\
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\lstick[3]{$\ket{\psi}$} & \xerr & \ctrl{3} & & & & & & \\
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& \xerr & & \ctrl{2} & \ctrl{3} & & & & \\
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& \xerr & & & & \ctrl{2} & & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & \xerr & \meter{} & \setwiretype{c} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & \xerr & \meter{} & \setwiretype{c}
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@@ -76,8 +76,8 @@
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\centering
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% tex-fmt: off
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\begin{quantikz}[row sep=4mm, column sep=2mm]
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& \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \\
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\lstick{$\ket{\psi}$} & \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \\
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\lstick[3]{$\ket{\psi}$} & \xyzerr & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & & & & & \\
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& \xyzerr & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & \ctrl{3} & \xyzerr \wire[d][3]{q} & & & & & \\
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& \xyzerr & & & & & & & \ctrl{2} & \xyzerr \wire[d][2]{q} & & & \\
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\lstick{$\ket{0}_{\text{A}_1}$} & \xyzerr & \targ{} & \xyzerr & \targ{} & \xyzerr & & & & & \xerr & \meter{} & \setwiretype{c} \\
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\lstick{$\ket{0}_{\text{A}_2}$} & \xyzerr & & & & & \targ{} & \xyzerr & \targ{} & \xyzerr & \xerr & \meter{} & \setwiretype{c}
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@@ -358,7 +358,7 @@
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% tex-fmt: on
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\caption{
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Repeated syndrome extraction circuit for the two-qubit
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Repeated syndrome extraction circuit for the three-qubit
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repetition code under phenomenological noise.
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}
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\end{figure}
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@@ -442,397 +442,3 @@
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\caption{Construction of detectors from measurements in the general case.}
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\end{figure}
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\begin{figure}[t]
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\centering
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\hspace*{-114mm}%
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\begin{tikzpicture}
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\draw[decorate, decoration={brace, amplitude=10pt}, line width=1pt]
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(0,0) -- (3.1,0) node[midway, above=4mm] {Commit region};
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\end{tikzpicture}
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\centering
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\includegraphics[scale=0.75]{res/72_bb_dem.pdf}
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\vspace*{-25.3mm}
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\hspace*{-98mm}%
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\begin{tikzpicture}
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\draw[{Latex}-{Latex}, line width=.7pt] (0, -0.75mm) -- (0, 5mm);
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\draw[line width=1pt] (-1mm,-0.75mm) -- (3mm,-0.75mm);
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\draw[line width=1pt] (-1mm,5mm) -- (3mm,5mm);
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\node[left] at (-2mm,2.125mm) {$\sim W$};
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\draw[{Latex}-{Latex}, line width=.3pt] (6.5cm,1.6mm) -- (6.5cm,5mm);
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\draw[line width=1pt] (6.5cm,4.9mm) -- (6.5cm,7mm);
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\node[above] at (6.5cm,7mm) {$\sim F$};
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\end{tikzpicture}
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\vspace*{10mm}
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\caption{
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Visualization of the windowing process on the detector
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error matrix.
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}
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\label{fig:windowing_pcm}
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\end{figure}
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\begin{figure}[t]
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\centering
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\tikzset{
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VN/.style={
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circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
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},
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CN/.style={
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rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
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},
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}
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\begin{tikzpicture}[node distance = 5mm]
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\node[VN] (vn00) {};
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\node[VN, below = of vn00] (vn01) {};
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\node[VN, below = of vn01] (vn02) {};
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\node[VN, below = of vn02] (vn03) {};
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\node[VN, below = of vn03] (vn04) {};
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\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
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\node[CN, left =10mm of temp] (cn00) {};
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\node[CN, below = of cn00] (cn01) {};
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\draw (vn00) -- (cn00);
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\draw (vn01) -- (cn00);
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\draw (vn03) -- (cn00);
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\draw (vn01) -- (cn01);
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\draw (vn02) -- (cn01);
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\draw (vn04) -- (cn01);
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\foreach \i in {1,2,3,4} {
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\pgfmathtruncatemacro{\prev}{\i-1}
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\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
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\node[VN, below = of vn\i0] (vn\i1) {};
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\node[VN, below = of vn\i1] (vn\i2) {};
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\node[VN, below = of vn\i2] (vn\i3) {};
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\node[VN, below = of vn\i3] (vn\i4) {};
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\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
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\node[CN, left = 10mm of temp] (cn\i0) {};
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\node[CN, below = of cn\i0] (cn\i1) {};
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\draw (vn\i0) -- (cn\i0);
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\draw (vn\i1) -- (cn\i0);
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\draw (vn\i3) -- (cn\i0);
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\draw (vn\i1) -- (cn\i1);
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\draw (vn\i2) -- (cn\i1);
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\draw (vn\i4) -- (cn\i1);
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}
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\foreach \i in {1,2,3,4} {
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\pgfmathtruncatemacro{\prev}{\i-1}
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\draw (vn\prev 3) -- (cn\i 0);
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\draw (vn\prev 4) -- (cn\i 1);
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}
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\node[
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draw, inner sep=5mm,line width=1pt,
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fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
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]
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(box1) {};
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\node[
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draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
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fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
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]
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(box2) {};
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% Marker for W on the bottom
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\draw[line width=1pt]
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([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
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coordinate (dim1l);
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\draw[line width=1pt]
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([yshift=-5mm]box1.south east) -- ++(0,-4mm)
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coordinate (dim1r);
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\draw[{Latex}-{Latex}, line width=1pt]
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([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
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node[midway, below=2pt] {$W$};
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% Marker for F on top
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\draw[line width=1pt]
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([yshift=3mm]box2.north west) -- ++(0,4mm)
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coordinate (dim3l);
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\draw[line width=1pt]
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([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
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coordinate (dim3r);
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\draw[{Latex}-{Latex}, line width=1pt]
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([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
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node[midway, above=2pt] {$F$};
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% Arrow on the top right
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\draw[-{Latex}, line width=1pt]
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([yshift=8mm] box1.north east) -- ++(28mm,0);
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\end{tikzpicture}
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\caption{Visualization of the windowing process on the Tanner graph.}
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\label{fig:windowing_tanner}
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\end{figure}
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\begin{figure}[t]
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\centering
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|
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\tikzset{
|
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VN/.style={
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circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
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},
|
||||
CN/.style={
|
||||
rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
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||||
},
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||||
}
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||||
|
||||
\begin{tikzpicture}[node distance = 5mm]
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\node[VN] (vn00) {};
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\node[VN, below = of vn00] (vn01) {};
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\node[VN, below = of vn01] (vn02) {};
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\node[VN, below = of vn02] (vn03) {};
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\node[VN, below = of vn03] (vn04) {};
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\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
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\node[CN, left =10mm of temp] (cn00) {};
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\node[CN, below = of cn00] (cn01) {};
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\draw (vn00) -- (cn00);
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\draw (vn01) -- (cn00);
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\draw (vn03) -- (cn00);
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\draw (vn01) -- (cn01);
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\draw (vn02) -- (cn01);
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\draw (vn04) -- (cn01);
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|
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\foreach \i in {1,2,3,4} {
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\pgfmathtruncatemacro{\prev}{\i-1}
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|
||||
\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
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||||
\node[VN, below = of vn\i0] (vn\i1) {};
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||||
\node[VN, below = of vn\i1] (vn\i2) {};
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\node[VN, below = of vn\i2] (vn\i3) {};
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||||
\node[VN, below = of vn\i3] (vn\i4) {};
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||||
|
||||
\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
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||||
|
||||
\node[CN, left = 10mm of temp] (cn\i0) {};
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||||
\node[CN, below = of cn\i0] (cn\i1) {};
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||||
|
||||
\draw (vn\i0) -- (cn\i0);
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||||
\draw (vn\i1) -- (cn\i0);
|
||||
\draw (vn\i3) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i1);
|
||||
\draw (vn\i2) -- (cn\i1);
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||||
\draw (vn\i4) -- (cn\i1);
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||||
}
|
||||
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||||
\foreach \i in {1,2,3,4} {
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\pgfmathtruncatemacro{\prev}{\i-1}
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||||
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||||
\draw (vn\prev 3) -- (cn\i 0);
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||||
\draw (vn\prev 4) -- (cn\i 1);
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||||
}
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||||
|
||||
\node[
|
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draw, inner sep=5mm,line width=1pt,
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||||
fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
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||||
]
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||||
(box1) {};
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||||
\node[
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||||
draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
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fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
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||||
]
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||||
(box2) {};
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||||
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn10);
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||||
\draw[KITorange, line width=2pt] (cn10) -- (vn11);
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||||
\draw[KITorange, line width=2pt] (cn10) -- (vn13);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn12);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn14);
|
||||
|
||||
\draw[KITorange, line width=2pt] (vn13) -- (cn20);
|
||||
\draw[KITorange, line width=2pt] (vn14) -- (cn21);
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn20);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn21);
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||||
\draw[KITorange, line width=2pt] (cn20) -- (vn23);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn22);
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||||
\draw[KITorange, line width=2pt] (cn21) -- (vn24);
|
||||
|
||||
% Marker for W on the bottom
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||||
\draw[line width=1pt]
|
||||
([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
|
||||
coordinate (dim1l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm]box1.south east) -- ++(0,-4mm)
|
||||
coordinate (dim1r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
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||||
node[midway, below=2pt] {$W$};
|
||||
|
||||
% Marker for F on top
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\draw[line width=1pt]
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||||
([yshift=3mm]box2.north west) -- ++(0,4mm)
|
||||
coordinate (dim3l);
|
||||
\draw[line width=1pt]
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||||
([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
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||||
coordinate (dim3r);
|
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\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
|
||||
node[midway, above=2pt] {$F$};
|
||||
|
||||
% Arrow on the top right
|
||||
\draw[-{Latex}, line width=1pt]
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||||
([yshift=8mm] box1.north east) -- ++(28mm,0);
|
||||
\end{tikzpicture}
|
||||
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\caption{
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Visualization of the messages used for the
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initialization of the next window.
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}
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\label{fig:messages_tanner}
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\end{figure}
|
||||
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
|
||||
\tikzset{
|
||||
VN/.style={
|
||||
circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
CN/.style={
|
||||
rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
}
|
||||
|
||||
\begin{tikzpicture}[node distance = 5mm]
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\node[VN, below = of vn03] (vn04) {};
|
||||
|
||||
\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
|
||||
|
||||
\node[CN, left =10mm of temp] (cn00) {};
|
||||
\node[CN, below = of cn00] (cn01) {};
|
||||
|
||||
\draw (vn00) -- (cn00);
|
||||
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|
||||
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|
||||
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|
||||
\draw (vn02) -- (cn01);
|
||||
\draw (vn04) -- (cn01);
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
|
||||
\node[VN, below = of vn\i0] (vn\i1) {};
|
||||
\node[VN, below = of vn\i1] (vn\i2) {};
|
||||
\node[VN, below = of vn\i2] (vn\i3) {};
|
||||
\node[VN, below = of vn\i3] (vn\i4) {};
|
||||
|
||||
\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
|
||||
|
||||
\node[CN, left = 10mm of temp] (cn\i0) {};
|
||||
\node[CN, below = of cn\i0] (cn\i1) {};
|
||||
|
||||
\draw (vn\i0) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i0);
|
||||
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|
||||
\draw (vn\i1) -- (cn\i1);
|
||||
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|
||||
\draw (vn\i4) -- (cn\i1);
|
||||
}
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\draw (vn\prev 3) -- (cn\i 0);
|
||||
\draw (vn\prev 4) -- (cn\i 1);
|
||||
}
|
||||
|
||||
\node[
|
||||
draw, inner sep=5mm,line width=1pt,
|
||||
fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
|
||||
]
|
||||
(box1) {};
|
||||
\node[
|
||||
draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
|
||||
fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
|
||||
]
|
||||
(box2) {};
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn10);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn13);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn12);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn14);
|
||||
|
||||
\draw[KITorange, line width=2pt] (vn13) -- (cn20);
|
||||
\draw[KITorange, line width=2pt] (vn14) -- (cn21);
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn20);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn23);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn22);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn24);
|
||||
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn10) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn11) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn12) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn13) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn14) {};
|
||||
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn20) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn21) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn22) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn23) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn24) {};
|
||||
|
||||
% Marker for W on the bottom
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
|
||||
coordinate (dim1l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm]box1.south east) -- ++(0,-4mm)
|
||||
coordinate (dim1r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
|
||||
node[midway, below=2pt] {$W$};
|
||||
|
||||
% Marker for F on top
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west) -- ++(0,4mm)
|
||||
coordinate (dim3l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
|
||||
coordinate (dim3r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
|
||||
node[midway, above=2pt] {$F$};
|
||||
|
||||
% Arrow on the top right
|
||||
\draw[-{Latex}, line width=1pt]
|
||||
([yshift=8mm] box1.north east) -- ++(28mm,0);
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{
|
||||
Visualization of the messages and decimation information used for the
|
||||
initialization of the next window.
|
||||
}
|
||||
\label{fig:messages_decimation_tanner}
|
||||
\end{figure}
|
||||
|
||||
|
||||
@@ -1,5 +1,407 @@
|
||||
\chapter{Decoding under Detector Error Models}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Sliding-Window Decoding}
|
||||
\section{Treating Detector Error Matrices like SC-LDPC Codes}
|
||||
\section{Soft-Information Aware Sliding-Window Decoding}
|
||||
\section{Numerical Results and Analysis}
|
||||
\label{sec:Sliding-Window Decoding}
|
||||
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
|
||||
\hspace*{-114mm}%
|
||||
\begin{tikzpicture}
|
||||
\draw[decorate, decoration={brace, amplitude=10pt}, line width=1pt]
|
||||
(0,0) -- (3.1,0) node[midway, above=4mm] {Commit region};
|
||||
\end{tikzpicture}
|
||||
|
||||
\centering
|
||||
\includegraphics[scale=0.75]{res/72_bb_dem.pdf}
|
||||
|
||||
\vspace*{-25.3mm}
|
||||
|
||||
\hspace*{-98mm}%
|
||||
\begin{tikzpicture}
|
||||
\draw[{Latex}-{Latex}, line width=.7pt] (0, -0.75mm) -- (0, 5mm);
|
||||
\draw[line width=1pt] (-1mm,-0.75mm) -- (3mm,-0.75mm);
|
||||
\draw[line width=1pt] (-1mm,5mm) -- (3mm,5mm);
|
||||
\node[left] at (-2mm,2.125mm) {$\sim W$};
|
||||
|
||||
\draw[{Latex}-{Latex}, line width=.3pt] (6.5cm,1.6mm) -- (6.5cm,5mm);
|
||||
\draw[line width=1pt] (6.5cm,4.9mm) -- (6.5cm,7mm);
|
||||
\node[above] at (6.5cm,7mm) {$\sim F$};
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{10mm}
|
||||
|
||||
\caption{
|
||||
Visualization of the windowing process on the detector
|
||||
error matrix.
|
||||
}
|
||||
\label{fig:windowing_pcm}
|
||||
\end{figure}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Warm-Start Sliding-Window Decoding under BP}
|
||||
\label{sec:warm_start_bp}
|
||||
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
|
||||
\tikzset{
|
||||
VN/.style={
|
||||
circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
CN/.style={
|
||||
rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
}
|
||||
|
||||
\begin{tikzpicture}[node distance = 5mm]
|
||||
\node[VN] (vn00) {};
|
||||
\node[VN, below = of vn00] (vn01) {};
|
||||
\node[VN, below = of vn01] (vn02) {};
|
||||
\node[VN, below = of vn02] (vn03) {};
|
||||
\node[VN, below = of vn03] (vn04) {};
|
||||
|
||||
\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
|
||||
|
||||
\node[CN, left =10mm of temp] (cn00) {};
|
||||
\node[CN, below = of cn00] (cn01) {};
|
||||
|
||||
\draw (vn00) -- (cn00);
|
||||
\draw (vn01) -- (cn00);
|
||||
\draw (vn03) -- (cn00);
|
||||
\draw (vn01) -- (cn01);
|
||||
\draw (vn02) -- (cn01);
|
||||
\draw (vn04) -- (cn01);
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
|
||||
\node[VN, below = of vn\i0] (vn\i1) {};
|
||||
\node[VN, below = of vn\i1] (vn\i2) {};
|
||||
\node[VN, below = of vn\i2] (vn\i3) {};
|
||||
\node[VN, below = of vn\i3] (vn\i4) {};
|
||||
|
||||
\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
|
||||
|
||||
\node[CN, left = 10mm of temp] (cn\i0) {};
|
||||
\node[CN, below = of cn\i0] (cn\i1) {};
|
||||
|
||||
\draw (vn\i0) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i0);
|
||||
\draw (vn\i3) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i1);
|
||||
\draw (vn\i2) -- (cn\i1);
|
||||
\draw (vn\i4) -- (cn\i1);
|
||||
}
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\draw (vn\prev 3) -- (cn\i 0);
|
||||
\draw (vn\prev 4) -- (cn\i 1);
|
||||
}
|
||||
|
||||
\node[
|
||||
draw, inner sep=5mm,line width=1pt,
|
||||
fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
|
||||
]
|
||||
(box1) {};
|
||||
\node[
|
||||
draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
|
||||
fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
|
||||
]
|
||||
(box2) {};
|
||||
|
||||
% Marker for W on the bottom
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
|
||||
coordinate (dim1l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm]box1.south east) -- ++(0,-4mm)
|
||||
coordinate (dim1r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
|
||||
node[midway, below=2pt] {$W$};
|
||||
|
||||
% Marker for F on top
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west) -- ++(0,4mm)
|
||||
coordinate (dim3l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
|
||||
coordinate (dim3r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
|
||||
node[midway, above=2pt] {$F$};
|
||||
|
||||
% Arrow on the top right
|
||||
\draw[-{Latex}, line width=1pt]
|
||||
([yshift=8mm] box1.north east) -- ++(28mm,0);
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Visualization of the windowing process on the Tanner graph.}
|
||||
\label{fig:windowing_tanner}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
|
||||
\tikzset{
|
||||
VN/.style={
|
||||
circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
CN/.style={
|
||||
rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
}
|
||||
|
||||
\begin{tikzpicture}[node distance = 5mm]
|
||||
\node[VN] (vn00) {};
|
||||
\node[VN, below = of vn00] (vn01) {};
|
||||
\node[VN, below = of vn01] (vn02) {};
|
||||
\node[VN, below = of vn02] (vn03) {};
|
||||
\node[VN, below = of vn03] (vn04) {};
|
||||
|
||||
\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
|
||||
|
||||
\node[CN, left =10mm of temp] (cn00) {};
|
||||
\node[CN, below = of cn00] (cn01) {};
|
||||
|
||||
\draw (vn00) -- (cn00);
|
||||
\draw (vn01) -- (cn00);
|
||||
\draw (vn03) -- (cn00);
|
||||
\draw (vn01) -- (cn01);
|
||||
\draw (vn02) -- (cn01);
|
||||
\draw (vn04) -- (cn01);
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
|
||||
\node[VN, below = of vn\i0] (vn\i1) {};
|
||||
\node[VN, below = of vn\i1] (vn\i2) {};
|
||||
\node[VN, below = of vn\i2] (vn\i3) {};
|
||||
\node[VN, below = of vn\i3] (vn\i4) {};
|
||||
|
||||
\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
|
||||
|
||||
\node[CN, left = 10mm of temp] (cn\i0) {};
|
||||
\node[CN, below = of cn\i0] (cn\i1) {};
|
||||
|
||||
\draw (vn\i0) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i0);
|
||||
\draw (vn\i3) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i1);
|
||||
\draw (vn\i2) -- (cn\i1);
|
||||
\draw (vn\i4) -- (cn\i1);
|
||||
}
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\draw (vn\prev 3) -- (cn\i 0);
|
||||
\draw (vn\prev 4) -- (cn\i 1);
|
||||
}
|
||||
|
||||
\node[
|
||||
draw, inner sep=5mm,line width=1pt,
|
||||
fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
|
||||
]
|
||||
(box1) {};
|
||||
\node[
|
||||
draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
|
||||
fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
|
||||
]
|
||||
(box2) {};
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn10);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn13);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn12);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn14);
|
||||
|
||||
\draw[KITorange, line width=2pt] (vn13) -- (cn20);
|
||||
\draw[KITorange, line width=2pt] (vn14) -- (cn21);
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn20);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn23);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn22);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn24);
|
||||
|
||||
% Marker for W on the bottom
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
|
||||
coordinate (dim1l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm]box1.south east) -- ++(0,-4mm)
|
||||
coordinate (dim1r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
|
||||
node[midway, below=2pt] {$W$};
|
||||
|
||||
% Marker for F on top
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west) -- ++(0,4mm)
|
||||
coordinate (dim3l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
|
||||
coordinate (dim3r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
|
||||
node[midway, above=2pt] {$F$};
|
||||
|
||||
% Arrow on the top right
|
||||
\draw[-{Latex}, line width=1pt]
|
||||
([yshift=8mm] box1.north east) -- ++(28mm,0);
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{
|
||||
Visualization of the messages used for the
|
||||
initialization of the next window.
|
||||
}
|
||||
\label{fig:messages_tanner}
|
||||
\end{figure}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Warm-Start Sliding-Window Decoding under BPGD}
|
||||
\label{sec:warm_start_bpgd}
|
||||
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
|
||||
\tikzset{
|
||||
VN/.style={
|
||||
circle, fill=KITgreen, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
CN/.style={
|
||||
rectangle, fill=KITblue, minimum width=1mm, minimum height=1mm,
|
||||
},
|
||||
}
|
||||
|
||||
\begin{tikzpicture}[node distance = 5mm]
|
||||
\node[VN] (vn00) {};
|
||||
\node[VN, below = of vn00] (vn01) {};
|
||||
\node[VN, below = of vn01] (vn02) {};
|
||||
\node[VN, below = of vn02] (vn03) {};
|
||||
\node[VN, below = of vn03] (vn04) {};
|
||||
|
||||
\coordinate (temp) at ($(vn01)!0.5!(vn02)$);
|
||||
|
||||
\node[CN, left =10mm of temp] (cn00) {};
|
||||
\node[CN, below = of cn00] (cn01) {};
|
||||
|
||||
\draw (vn00) -- (cn00);
|
||||
\draw (vn01) -- (cn00);
|
||||
\draw (vn03) -- (cn00);
|
||||
\draw (vn01) -- (cn01);
|
||||
\draw (vn02) -- (cn01);
|
||||
\draw (vn04) -- (cn01);
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\node[VN, right = 25mm of vn\prev 0] (vn\i0) {};
|
||||
\node[VN, below = of vn\i0] (vn\i1) {};
|
||||
\node[VN, below = of vn\i1] (vn\i2) {};
|
||||
\node[VN, below = of vn\i2] (vn\i3) {};
|
||||
\node[VN, below = of vn\i3] (vn\i4) {};
|
||||
|
||||
\coordinate (temp) at ($(vn\i1)!0.5!(vn\i2)$);
|
||||
|
||||
\node[CN, left = 10mm of temp] (cn\i0) {};
|
||||
\node[CN, below = of cn\i0] (cn\i1) {};
|
||||
|
||||
\draw (vn\i0) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i0);
|
||||
\draw (vn\i3) -- (cn\i0);
|
||||
\draw (vn\i1) -- (cn\i1);
|
||||
\draw (vn\i2) -- (cn\i1);
|
||||
\draw (vn\i4) -- (cn\i1);
|
||||
}
|
||||
|
||||
\foreach \i in {1,2,3,4} {
|
||||
\pgfmathtruncatemacro{\prev}{\i-1}
|
||||
|
||||
\draw (vn\prev 3) -- (cn\i 0);
|
||||
\draw (vn\prev 4) -- (cn\i 1);
|
||||
}
|
||||
|
||||
\node[
|
||||
draw, inner sep=5mm,line width=1pt,
|
||||
fit=(vn00)(vn04)(cn00)(cn01)(vn20)(vn24)(cn20)(cn21)
|
||||
]
|
||||
(box1) {};
|
||||
\node[
|
||||
draw, dashed, inner sep=5mm, inner ysep=8mm,line width=1pt,
|
||||
fit=(vn10)(vn14)(cn10)(cn11)(vn30)(vn34)(cn30)(cn31)
|
||||
]
|
||||
(box2) {};
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn10);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn10) -- (vn13);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn11);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn12);
|
||||
\draw[KITorange, line width=2pt] (cn11) -- (vn14);
|
||||
|
||||
\draw[KITorange, line width=2pt] (vn13) -- (cn20);
|
||||
\draw[KITorange, line width=2pt] (vn14) -- (cn21);
|
||||
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn20);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn20) -- (vn23);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn21);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn22);
|
||||
\draw[KITorange, line width=2pt] (cn21) -- (vn24);
|
||||
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn10) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn11) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn12) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn13) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn14) {};
|
||||
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn20) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn21) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn22) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn23) {};
|
||||
\node[VN, draw=KITorange, fill=KITorange] at (vn24) {};
|
||||
|
||||
% Marker for W on the bottom
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm, line width=1pt]box1.south west) -- ++(0,-4mm)
|
||||
coordinate (dim1l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=-5mm]box1.south east) -- ++(0,-4mm)
|
||||
coordinate (dim1r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=1mm]dim1l) -- ([yshift=1mm]dim1r)
|
||||
node[midway, below=2pt] {$W$};
|
||||
|
||||
% Marker for F on top
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west) -- ++(0,4mm)
|
||||
coordinate (dim3l);
|
||||
\draw[line width=1pt]
|
||||
([yshift=3mm]box2.north west -| box1.north west) -- ++(0,4mm)
|
||||
coordinate (dim3r);
|
||||
\draw[{Latex}-{Latex}, line width=1pt]
|
||||
([yshift=-1mm]dim3l) -- ([yshift=-1mm]dim3r)
|
||||
node[midway, above=2pt] {$F$};
|
||||
|
||||
% Arrow on the top right
|
||||
\draw[-{Latex}, line width=1pt]
|
||||
([yshift=8mm] box1.north east) -- ++(28mm,0);
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{
|
||||
Visualization of the messages and decimation information used for the
|
||||
initialization of the next window.
|
||||
}
|
||||
\label{fig:messages_decimation_tanner}
|
||||
\end{figure}
|
||||
|
||||
|
||||
@@ -100,11 +100,11 @@
|
||||
\tableofcontents
|
||||
\cleardoublepage
|
||||
|
||||
% \input{chapters/1_introduction.tex}
|
||||
% \input{chapters/2_fundamentals.tex}
|
||||
\input{chapters/1_introduction.tex}
|
||||
\input{chapters/2_fundamentals.tex}
|
||||
\input{chapters/3_fault_tolerant_qec.tex}
|
||||
% \input{chapters/4_decoding_under_dems.tex}
|
||||
% \input{chapters/5_conclusion_and_outlook.tex}
|
||||
\input{chapters/4_decoding_under_dems.tex}
|
||||
\input{chapters/5_conclusion_and_outlook.tex}
|
||||
|
||||
% \appendix
|
||||
% \listoffigures
|
||||
|
||||
Reference in New Issue
Block a user