diff --git a/src/final_presentation/main.tex b/src/final_presentation/main.tex index 17b3a52..e5d84fe 100644 --- a/src/final_presentation/main.tex +++ b/src/final_presentation/main.tex @@ -1759,7 +1759,9 @@ \label{subsec:Soft-Information-Aware Sliding-Window Decoding} \begin{frame} - \frametitle{Warm-Start Sliding-Window Decoding} + \frametitle{BP: Warm-Start Sliding-Window Decoding} + + \vspace*{-15mm} \begin{itemize} \item Contribution: \schlagwort{Warm-start} by initializing @@ -1782,6 +1784,7 @@ }, } + \only<1>{ \begin{tikzpicture}[node distance = 7mm] \node[VN] (vn00) {}; \node[VN, below = of vn00] (vn01) {}; @@ -1867,13 +1870,117 @@ \draw[-{Latex}, line width=1pt] ([yshift=8mm] box1.north east) -- ++(35mm,0); \end{tikzpicture} + }% + \only<2->{ + \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) {}; + + \draw[kit-orange, line width=2pt] (cn10) -- (vn10); + \draw[kit-orange, line width=2pt] (cn10) -- (vn11); + \draw[kit-orange, line width=2pt] (cn10) -- (vn13); + \draw[kit-orange, line width=2pt] (cn11) -- (vn11); + \draw[kit-orange, line width=2pt] (cn11) -- (vn12); + \draw[kit-orange, line width=2pt] (cn11) -- (vn14); + + \draw[kit-orange, line width=2pt] (vn13) -- (cn20); + \draw[kit-orange, line width=2pt] (vn14) -- (cn21); + + \draw[kit-orange, line width=2pt] (cn20) -- (vn20); + \draw[kit-orange, line width=2pt] (cn20) -- (vn21); + \draw[kit-orange, line width=2pt] (cn20) -- (vn23); + \draw[kit-orange, line width=2pt] (cn21) -- (vn21); + \draw[kit-orange, line width=2pt] (cn21) -- (vn22); + \draw[kit-orange, line width=2pt] (cn21) -- (vn24); + + % 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 of overlapping region - to next window + \item Pass messages from overlapping region to next window \end{itemize} \end{frame} @@ -2883,6 +2990,243 @@ \stopreferencesendmanual \end{frame} +\begin{frame} + \frametitle{BPGD: Warm-Start Sliding-Window Decoding I} + + \vspace*{-15mm} + + \begin{itemize} + \item BPGD: Additional information about overlap region + \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, + }, + } + + \only<1>{ + \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} + }% + \only<2->{ + \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) {}; + + \draw[kit-orange, line width=2pt] (cn10) -- (vn10); + \draw[kit-orange, line width=2pt] (cn10) -- (vn11); + \draw[kit-orange, line width=2pt] (cn10) -- (vn13); + \draw[kit-orange, line width=2pt] (cn11) -- (vn11); + \draw[kit-orange, line width=2pt] (cn11) -- (vn12); + \draw[kit-orange, line width=2pt] (cn11) -- (vn14); + + \draw[kit-orange, line width=2pt] (vn13) -- (cn20); + \draw[kit-orange, line width=2pt] (vn14) -- (cn21); + + \draw[kit-orange, line width=2pt] (cn20) -- (vn20); + \draw[kit-orange, line width=2pt] (cn20) -- (vn21); + \draw[kit-orange, line width=2pt] (cn20) -- (vn23); + \draw[kit-orange, line width=2pt] (cn21) -- (vn21); + \draw[kit-orange, line width=2pt] (cn21) -- (vn22); + \draw[kit-orange, line width=2pt] (cn21) -- (vn24); + + \node[VN, draw=kit-orange, fill=kit-orange] at (vn10) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn11) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn12) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn13) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn14) {}; + + \node[VN, draw=kit-orange, fill=kit-orange] at (vn20) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn21) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn22) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn23) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn24) {}; + + % 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 messages \schlagwort{and decimation information} to next window + \end{itemize} +\end{frame} + \begin{frame} \frametitle{BPGD: Passing Decimation Information} @@ -2988,7 +3332,7 @@ \begin{itemize} \item $\llbracket 144,12,12\rrbracket$ \ac{bb} code \item $12$ \ac{se} rounds - \item \Ac{spa} + \ac{gd} decoder + \item \Ac{spa} + \ac{gd} \item Parameters \begin{itemize} \item $T = 1$ @@ -2999,6 +3343,260 @@ \end{minipage} \end{frame} +\begin{frame} + \frametitle{BPGD: Warm-Start Sliding-Window Decoding II} + + \vspace*{-15mm} + + \begin{itemize} + \item Decimation information: \schlagwort{Premature hard decision} on VNs + \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, + }, + } + + \only<1>{ + \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) {}; + + \draw[kit-orange, line width=2pt] (cn10) -- (vn10); + \draw[kit-orange, line width=2pt] (cn10) -- (vn11); + \draw[kit-orange, line width=2pt] (cn10) -- (vn13); + \draw[kit-orange, line width=2pt] (cn11) -- (vn11); + \draw[kit-orange, line width=2pt] (cn11) -- (vn12); + \draw[kit-orange, line width=2pt] (cn11) -- (vn14); + + \draw[kit-orange, line width=2pt] (vn13) -- (cn20); + \draw[kit-orange, line width=2pt] (vn14) -- (cn21); + + \draw[kit-orange, line width=2pt] (cn20) -- (vn20); + \draw[kit-orange, line width=2pt] (cn20) -- (vn21); + \draw[kit-orange, line width=2pt] (cn20) -- (vn23); + \draw[kit-orange, line width=2pt] (cn21) -- (vn21); + \draw[kit-orange, line width=2pt] (cn21) -- (vn22); + \draw[kit-orange, line width=2pt] (cn21) -- (vn24); + + \node[VN, draw=kit-orange, fill=kit-orange] at (vn10) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn11) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn12) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn13) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn14) {}; + + \node[VN, draw=kit-orange, fill=kit-orange] at (vn20) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn21) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn22) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn23) {}; + \node[VN, draw=kit-orange, fill=kit-orange] at (vn24) {}; + + % 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} + }% + \only<2->{ + \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) {}; + + \draw[kit-orange, line width=2pt] (cn10) -- (vn10); + \draw[kit-orange, line width=2pt] (cn10) -- (vn11); + \draw[kit-orange, line width=2pt] (cn10) -- (vn13); + \draw[kit-orange, line width=2pt] (cn11) -- (vn11); + \draw[kit-orange, line width=2pt] (cn11) -- (vn12); + \draw[kit-orange, line width=2pt] (cn11) -- (vn14); + + \draw[kit-orange, line width=2pt] (vn13) -- (cn20); + \draw[kit-orange, line width=2pt] (vn14) -- (cn21); + + \draw[kit-orange, line width=2pt] (cn20) -- (vn20); + \draw[kit-orange, line width=2pt] (cn20) -- (vn21); + \draw[kit-orange, line width=2pt] (cn20) -- (vn23); + \draw[kit-orange, line width=2pt] (cn21) -- (vn21); + \draw[kit-orange, line width=2pt] (cn21) -- (vn22); + \draw[kit-orange, line width=2pt] (cn21) -- (vn24); + + % 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 \schlagwort{only messages} to next window + \end{itemize} +\end{frame} + \begin{frame} \frametitle{BPGD Performance: Window Size}