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Add sliding window Tanner graph and BPGD slides

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This commit is contained in:
Andreas Tsouchlos
2026-04-17 15:02:21 +02:00
parent 9b60bfc4ee
commit 2aa4bdc1b5
6 changed files with 274 additions and 42 deletions
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240
src/final_presentation/main.tex
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@@ -154,6 +154,16 @@
long=belief propagation
}
\DeclareAcronym{vn}{
short=VN,
long=variable node
}
\DeclareAcronym{cn}{
short=CN,
long=check node
}
\DeclareAcronym{spa}{
short=SPA,
long=sum-product algorithm
@@ -1760,11 +1770,12 @@
\schlagwort{commit region} (part of the
window with no overlap)
\item \schlagwort{update syndrome} of overlapping region
\item move to next window
\end{itemize}
}
\end{itemize}
\vspace*{20mm}
\vspace*{12mm}
\addreferencesmanual
{HP23}{
@@ -1784,6 +1795,124 @@
\subsection{Soft-Information-Aware Sliding-Window Decoding}
\label{subsec:Soft-Information-Aware Sliding-Window Decoding}
\begin{frame}
\frametitle{Soft-Information-Aware Sliding-Window\\ Decoding}
\begin{itemize}
\item Perform \schlagwort{warm-start} by initializing with
soft information from previous window
\end{itemize}
\vspace*{-5mm}
\begin{figure}[H]
\centering
\tikzset{
VN/.style={
circle, fill=kit-green,
inner sep=1.5mm,
},
CN/.style={
rectangle, fill=kit-blue,
inner sep=1.8mm,
},
}
\begin{tikzpicture}[node distance = 7mm]
\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 =15mm 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 = 35mm 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 = 15mm 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 solid box (positions 0–2)
\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=-2mm]dim1l) -- ([yshift=-2mm]dim1r)
node[midway, below=2pt] {$W$};
% Marker for step size 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=2mm]dim3l) -- ([yshift=2mm]dim3r)
node[midway, above=2pt] {$F$};
\draw[-{Latex}, line width=1pt] ([yshift=8mm] box1.north
east) -- ++(35mm,0);
\end{tikzpicture}
\end{figure}
\vspace*{-5mm}
\begin{itemize}
\item Pass \ac{cn} to \ac{vn} messages
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{BP Performance: Window Size I}
@@ -2611,33 +2740,89 @@ opacity=0.4]
\begin{frame}[fragile]
\frametitle{BP with Guided Decimation}
\begin{minipage}{0.5\textwidth}
\vspace*{-10mm}
\centering
\begin{itemize}
\item After every $T$ \ac{bp} iterations, fix most reliable
variable node
\item After every $T$ \ac{bp} iterations
\citereferencemanual{YLH+24}
\begin{itemize}
\item perform hard decision on most reliable \ac{vn}
\item exclude \ac{vn} from further decoding
\end{itemize}
\vspace*{10mm}
\item Mitigates problems due to degeneracy \\
$\rightarrow$ Decoder is encouraged to focus on \\
\hspace{9mm} one solution
\end{itemize}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\visible<2->{
\centering
\vspace*{-10mm}
\begin{itemize}
\item $[[882, 24, 18 \le d \le 24]]$ - generalized
hypergraph product (GHP) code, \\
bit-flip noise \citereferencemanual{YLH+24}
\end{itemize}
% \begin{minipage}{0.65\textwidth}
% \centering
% \begin{algorithm}[H]
% \caption{BP with guided decimation (BPGD)
% \citereferencemanual{YLH+24}}
% \begin{algorithmic}[1]
% \STATE \textbf{for} $r=1$ \textbf{to} $n$ \textbf{do}
% \STATE \hspace{5mm} Run $T$ BP iterations
% \STATE $\hat{x} \leftarrow$
% \STATE \textbf{done}
% \end{algorithmic}
% \end{algorithm}
% \end{minipage}%
% \begin{minipage}{0.35\textwidth}
% \centering
% \begin{itemize}
% \item asdf
% \end{itemize}
% \end{minipage}
\vspace*{-5mm}
\vspace*{15mm}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
width=13cm,
height=9cm,
ymode=log,
legend pos = south east,
ymin=1e-6, ymax=1,
enlargelimits=false,
legend style={
cells={anchor=west},
cells={align=left},
},
xlabel = {Physical error rate},
ylabel = {Frame error rate},
xtick={0.04,0.05,...,0.1},
xticklabel style={/pgf/number format/fixed},
xticklabel style={/pgf/number format/precision=4},
grid=both,
]
\addplot+[mark=o, line width=2pt, black]
table[col sep=comma, x=p, y=FER]
{res/literature/yao_bp.csv};
\addlegendentry{BP}
\addplot+[mark=o, line width=2pt, kit-green]
table[col sep=comma, x=p, y=FER]
{res/literature/yao_bpgd_1.csv};
\addlegendentry{BPGD, $T = 1$}
\addplot+[mark=o, line width=2pt, kit-red]
table[col sep=comma, x=p, y=FER]
{res/literature/yao_bpgd_10.csv};
\addlegendentry{BPGD, $T = 10$}
\addplot+[mark=o, line width=2pt, kit-blue]
table[col sep=comma, x=p, y=FER]
{res/literature/yao_bpgd_70.csv};
\addlegendentry{BPGD, $T = 70$}
\addplot+[mark=o, line width=2pt, kit-orange]
table[col sep=comma, x=p, y=FER]
{res/literature/yao_bpgd_100.csv};
\addlegendentry{BPGD, $T = 100$}
\end{axis}
\end{tikzpicture}
\end{figure}
}
\end{minipage}
\vspace*{2mm}
\addreferencesmanual
{YLH+24}{Hanwen Yao et al. ``Belief propagation decoding of quantum
@@ -2849,6 +3034,7 @@ forget plot]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $n_\text{iterations} = 200$
\item $F = 1$
\end{itemize}
@@ -2985,6 +3171,7 @@ forget plot]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $n_\text{iterations} = n $
\item $F = 1$
\end{itemize}
@@ -3076,6 +3263,7 @@ forget plot]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $p = 0.0025$
\item $F = 1$
\end{itemize}
@@ -3167,6 +3355,7 @@ forget plot]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $n_\text{iterations} = 32$
\item $W = 5$
\end{itemize}
@@ -3271,6 +3460,7 @@ opacity=0.4]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $n_\text{iterations} = 200$
\item $W = 5$
\end{itemize}
@@ -3375,6 +3565,7 @@ opacity=0.4]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $n_\text{iterations} = 5000$
\item $W = 5$
\end{itemize}
@@ -3466,6 +3657,7 @@ opacity=0.4]
\item \ac{spa} + \ac{gd} decoder
\item Parameters
\begin{itemize}
\item $T = 1$
\item $p = 0.0025$
\item $W = 5$
\end{itemize}
@@ -3780,7 +3972,7 @@ opacity=0.4]
\begin{itemize}
\item BP with guided decimation (BPGD) \\
$\rightarrow$ Iteratively fix most reliable
variable node (VN)
\ac{vn}
\vspace*{10mm}
\item \schlagwort{Guided decimation guessing} (GDG)
\citereferencemanual{GCR24}

8
src/final_presentation/res/literature/yao_bp.csv Normal file
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@@ -0,0 +1,8 @@
p, FER
0.040000, 0.043667
0.049986, 0.087737
0.059972, 0.148066
0.069958, 0.255386
0.079945, 0.460128
0.089931, 0.759770
0.100000, 0.965714
1 p FER
2 0.040000 0.043667
3 0.049986 0.087737
4 0.059972 0.148066
5 0.069958 0.255386
6 0.079945 0.460128
7 0.089931 0.759770
8 0.100000 0.965714

8
src/final_presentation/res/literature/yao_bpgd_1.csv Normal file
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@@ -0,0 +1,8 @@
p, FER
0.040083, 0.000029
0.049986, 0.000393
0.059972, 0.006271
0.069958, 0.055503
0.080028, 0.244488
0.090014, 0.559895
0.100000, 0.904565
1 p FER
2 0.040083 0.000029
3 0.049986 0.000393
4 0.059972 0.006271
5 0.069958 0.055503
6 0.080028 0.244488
7 0.090014 0.559895
8 0.100000 0.904565

8
src/final_presentation/res/literature/yao_bpgd_10.csv Normal file
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@@ -0,0 +1,8 @@
p, FER
0.039917, 0.000006
0.049986, 0.000179
0.059972, 0.003882
0.070042, 0.038312
0.080028, 0.229007
0.090014, 0.610921
0.100083, 0.885054
1 p FER
2 0.039917 0.000006
3 0.049986 0.000179
4 0.059972 0.003882
5 0.070042 0.038312
6 0.080028 0.229007
7 0.090014 0.610921
8 0.100083 0.885054

8
src/final_presentation/res/literature/yao_bpgd_100.csv Normal file
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@@ -0,0 +1,8 @@
p, FER
0.040083, 0.000001
0.050153, 0.000095
0.060139, 0.003121
0.070125, 0.036677
0.079945, 0.255386
0.090014, 0.513130
0.100000, 0.847287
1 p FER
2 0.040083 0.000001
3 0.050153 0.000095
4 0.060139 0.003121
5 0.070125 0.036677
6 0.079945 0.255386
7 0.090014 0.513130
8 0.100000 0.847287

8
src/final_presentation/res/literature/yao_bpgd_70.csv Normal file
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@@ -0,0 +1,8 @@
p, FER
0.040000, 0.000002
0.049986, 0.000119
0.060055, 0.003716
0.069958, 0.042725
0.080111, 0.224068
0.090014, 0.572237
0.100000, 0.904565
1 p FER
2 0.040000 0.000002
3 0.049986 0.000119
4 0.060055 0.003716
5 0.069958 0.042725
6 0.080111 0.224068
7 0.090014 0.572237
8 0.100000 0.904565