From 6afa41ae0a051dafc7c75eb9b88c8e0e0a622aed Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Fri, 17 Apr 2026 23:05:31 +0200 Subject: [PATCH] Add edge annotations to workflow overview figure --- src/final_presentation/main.tex | 557 ++++++++++++++++---------------- 1 file changed, 279 insertions(+), 278 deletions(-) diff --git a/src/final_presentation/main.tex b/src/final_presentation/main.tex index ec2f7b5..d120117 100644 --- a/src/final_presentation/main.tex +++ b/src/final_presentation/main.tex @@ -55,7 +55,7 @@ \usepackage{algorithm} \title{Fault Tolerant Quantum Error Correction} -\subtitle{Master's Thesis Midterm Presentation} +\subtitle{Master's Thesis Final Presentation} \author[ Andreas]{Andreas Tsouchlos} \date[]{} @@ -537,16 +537,16 @@ \coordinate (temp) at ($(enc)!0.5!(dec) + (-85mm,0)$); \node[block] (ler) at (temp) {LER calculation}; - \node (inp) at ($(enc) + (-140mm,0)$) {$\ket{\psi}_\text{L}$}; + \node (inp) at ($(enc) + (-140mm,0)$) {$\ket{\varphi}$}; \node (out) at ($(dec) + (-140mm,0)$) - {$\ket{\hat{\psi}}_\text{L}$}; + {$\ket{\hat{\varphi}}_\text{L}$}; \draw[-{Latex}] (inp) -- (enc); - \draw[-{Latex}] (enc) -- (cha); - \draw[-{Latex}] (cha) -- (syn); - \draw[-{Latex}] (syn) -- (sde); - \draw[-{Latex}] (sde) -- (rev); - \draw[-{Latex}] (rev) -- (dec); + \draw[-{Latex}] (enc) -- (cha) node[midway, above] {$\ket{\psi}$}; + \draw[-{Latex}] (cha) -- (syn) node[midway, above] {$\mathcal{E}\ket{\psi}$}; + \draw[-{Latex}] (syn) -- (sde) node[midway, right] {$\bm{s}$}; + \draw[-{Latex}] (sde) -- (rev) node[midway, above] {$\hat{\mathcal{E}}$}; + \draw[-{Latex}] (rev) -- (dec) node[midway, above] {$\ket{\hat{\psi}}$}; \draw[-{Latex}] (dec) -- (out); \draw[-{Latex}] (cha) -- (rev); @@ -558,7 +558,7 @@ } \end{figure} - \vspace*{10mm} + \vspace*{8mm} \visible<2->{ \begin{minipage}{0.35\textwidth} @@ -687,276 +687,276 @@ \subsection{Detector Error Models} \label{subsec:Detector Error Models} -\begin{frame}[fragile] - \frametitle{The Measurement Syndrome Matrix I} - - \vspace*{-18mm} - - \begin{itemize} - \item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\ - contains error patterns \citereferencemanual{DTB$^+$25} - \item Example: 3-qubit repetition code - \end{itemize} - - \vspace*{-25mm} - - \centering - \only<1>{ - \begin{minipage}{0.4\textwidth} - \centering - - \vspace*{40mm} - \begin{tikzpicture} - \node{$% - \bm{\Omega} = - \left( - \begin{array}{ccc} - 1 & 1 & 0 \\ - 0 & 1 & 1 \\ - 1 & 1 & 0 \\ - 0 & 1 & 1 \\ - 1 & 1 & 0 \\ - 0 & 1 & 1 - \end{array} - \right)$ - }; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,1.2) -- (2.5,2.85) - node[midway,right,xshift=10mm]{$\text{SE}_1$}; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,-0.75) -- (2.5,0.9) - node[midway,right,xshift=10mm]{$\text{SE}_2$}; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,-2.7) -- (2.5,-1.1) - node[midway,right,xshift=10mm]{$\text{SE}_3$}; - \end{tikzpicture} - - \vspace*{-10mm} - - \begin{gather*} - \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} - \end{gather*} - \end{minipage}% - \begin{minipage}{0.6\textwidth} - \begin{figure}[H] - \newcommand{\preperr}[1]{ - \gate[style={fill=orange!20}]{\scriptstyle ##1} - } - - \centering - - \begin{quantikz}[ - row sep=4mm, column sep=4mm, - wire types={q,q,q,q,q,n,n,n,n}, - execute at end picture={ - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-4-19.north east) - -- - (\tikzcdmatrixname-5-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_1$}; - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-6-19.north east) - -- - (\tikzcdmatrixname-7-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_2$}; - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-8-19.north east) - -- - (\tikzcdmatrixname-9-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_3$}; - } - ] - % tex-fmt: off - & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ - \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ - & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & & & & & & & \meter{} & \setwiretype{c} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} - % tex-fmt: on - \end{quantikz} - \end{figure} - \end{minipage} - } - \only<2>{ - \begin{minipage}{0.4\textwidth} - \centering - - \vspace*{40mm} - \begin{tikzpicture} - \node{$% - \bm{\Omega} = - \left( - \begin{array}{>{\columncolor{red!20}}ccc} - 1 & 1 & 0 \\ - 0 & 1 & 1 \\ - 1 & 1 & 0 \\ - 0 & 1 & 1 \\ - 1 & 1 & 0 \\ - 0 & 1 & 1 - \end{array} - \right)$ - }; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,1.2) -- (2.5,2.85) - node[midway,right,xshift=10mm]{$\text{SE}_1$}; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,-0.75) -- (2.5,0.9) - node[midway,right,xshift=10mm]{$\text{SE}_2$}; - - \draw [ - line width=1pt, - decorate, - decoration={brace,mirror,amplitude=3mm,raise=5mm} - ] - (2.5,-2.7) -- (2.5,-1.1) - node[midway,right,xshift=10mm]{$\text{SE}_3$}; - \end{tikzpicture} - - \vspace*{-10mm} - - \begin{gather*} - \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} - \end{gather*} - \end{minipage}% - \begin{minipage}{0.6\textwidth} - \begin{figure}[H] - \newcommand{\preperr}[1]{ - \gate[style={fill=orange!20}]{\scriptstyle ##1} - } - \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} - - \newcommand{\noise}{ - \gate[style={noisy}]{\text{\small X}}% - \setwiretype{n}% - \wire[l][1]{q} - } - \newcommand{\redwire}[1]{ - \wire[r][##1][style={draw=red, line width=2pt}]{q} - } - \newcommand{\redtarg}{ - \targ[style={draw=red}]{}% - \setwiretype{n}% - \wire[l][1]{q} - } - \newcommand{\redctrl}[1]{ - \ctrl[style={draw=red,fill=red,line width=2pt}]{##1} - } - \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} - - \tikzset{ - noisy/.style={ - starburst, - starburst point height=2mm, - fill=red!25, draw=red!85!black, - line width=2pt, - inner xsep=-2pt, inner ysep=-2pt - }, - } - - \centering - - \begin{quantikz}[ - row sep=4mm, column sep=4mm, - wire types={q,q,q,q,q,n,n,n,n}, - execute at end picture={ - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-4-19.north east) - -- - (\tikzcdmatrixname-5-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_1$}; - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-6-19.north east) - -- - (\tikzcdmatrixname-7-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_2$}; - \draw [ - line width=1pt, - decorate, - decoration={brace,amplitude=3mm,raise=9mm} - ] - (\tikzcdmatrixname-8-19.north east) - -- - (\tikzcdmatrixname-9-19.south east) - node[midway,right,xshift=14mm]{$\text{SE}_3$}; - } - ] - % tex-fmt: off - & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\ - \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ - & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ - \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ - \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg\redwire{10} & \targ{} & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ - & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \redtarg\redwire{4} & \targ{} & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ - & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} - % tex-fmt: on - \end{quantikz} - \end{figure} - \end{minipage} - } - - \vspace*{8mm} - - \addreferencesmanual - {DTB$^+$25}{ - P.- J. H. S. Derks et al., ``Designing fault-tolerant - circuits using detector error models,'' \emph{Quantum}, 2025. - } - \stopreferencesmanual -\end{frame} +% \begin{frame}[fragile] +% \frametitle{The Measurement Syndrome Matrix I} +% +% \vspace*{-18mm} +% +% \begin{itemize} +% \item \schlagwort{Measurement syndrome matrix} $\bm{\Omega}$ \\ +% contains error patterns \citereferencemanual{DTB$^+$25} +% \item Example: 3-qubit repetition code +% \end{itemize} +% +% \vspace*{-25mm} +% +% \centering +% \only<1>{ +% \begin{minipage}{0.4\textwidth} +% \centering +% +% \vspace*{40mm} +% \begin{tikzpicture} +% \node{$% +% \bm{\Omega} = +% \left( +% \begin{array}{ccc} +% 1 & 1 & 0 \\ +% 0 & 1 & 1 \\ +% 1 & 1 & 0 \\ +% 0 & 1 & 1 \\ +% 1 & 1 & 0 \\ +% 0 & 1 & 1 +% \end{array} +% \right)$ +% }; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,1.2) -- (2.5,2.85) +% node[midway,right,xshift=10mm]{$\text{SE}_1$}; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,-0.75) -- (2.5,0.9) +% node[midway,right,xshift=10mm]{$\text{SE}_2$}; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,-2.7) -- (2.5,-1.1) +% node[midway,right,xshift=10mm]{$\text{SE}_3$}; +% \end{tikzpicture} +% +% \vspace*{-10mm} +% +% \begin{gather*} +% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} +% \end{gather*} +% \end{minipage}% +% \begin{minipage}{0.6\textwidth} +% \begin{figure}[H] +% \newcommand{\preperr}[1]{ +% \gate[style={fill=orange!20}]{\scriptstyle ##1} +% } +% +% \centering +% +% \begin{quantikz}[ +% row sep=4mm, column sep=4mm, +% wire types={q,q,q,q,q,n,n,n,n}, +% execute at end picture={ +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-4-19.north east) +% -- +% (\tikzcdmatrixname-5-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_1$}; +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-6-19.north east) +% -- +% (\tikzcdmatrixname-7-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_2$}; +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-8-19.north east) +% -- +% (\tikzcdmatrixname-9-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_3$}; +% } +% ] +% % tex-fmt: off +% & \preperr{E_0} & \ctrl{3} & & & & & & \ctrl{5} & & & & & & \ctrl{7} & & & & & \\ +% \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ +% & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ +% \lstick{$\ket{0}_{\text{A}_1}$} & & \targ{} & \targ{} & & & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ +% \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ +% & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \targ{} & \targ{} & & & & & & & & & \meter{} & \setwiretype{c} \\ +% & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\ +% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \targ{} & \targ{} & & & \meter{} & \setwiretype{c} \\ +% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} +% % tex-fmt: on +% \end{quantikz} +% \end{figure} +% \end{minipage} +% } +% \only<2>{ +% \begin{minipage}{0.4\textwidth} +% \centering +% +% \vspace*{40mm} +% \begin{tikzpicture} +% \node{$% +% \bm{\Omega} = +% \left( +% \begin{array}{>{\columncolor{red!20}}ccc} +% 1 & 1 & 0 \\ +% 0 & 1 & 1 \\ +% 1 & 1 & 0 \\ +% 0 & 1 & 1 \\ +% 1 & 1 & 0 \\ +% 0 & 1 & 1 +% \end{array} +% \right)$ +% }; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,1.2) -- (2.5,2.85) +% node[midway,right,xshift=10mm]{$\text{SE}_1$}; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,-0.75) -- (2.5,0.9) +% node[midway,right,xshift=10mm]{$\text{SE}_2$}; +% +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,mirror,amplitude=3mm,raise=5mm} +% ] +% (2.5,-2.7) -- (2.5,-1.1) +% node[midway,right,xshift=10mm]{$\text{SE}_3$}; +% \end{tikzpicture} +% +% \vspace*{-10mm} +% +% \begin{gather*} +% \bm{s} \in \text{span} \mleft\{ \bm{\Omega} \mright\} +% \end{gather*} +% \end{minipage}% +% \begin{minipage}{0.6\textwidth} +% \begin{figure}[H] +% \newcommand{\preperr}[1]{ +% \gate[style={fill=orange!20}]{\scriptstyle ##1} +% } +% \newcommand{\measerr}{\gate[style={fill=blue!20}]{\phantom{1}}} +% +% \newcommand{\noise}{ +% \gate[style={noisy}]{\text{\small X}}% +% \setwiretype{n}% +% \wire[l][1]{q} +% } +% \newcommand{\redwire}[1]{ +% \wire[r][##1][style={draw=red, line width=2pt}]{q} +% } +% \newcommand{\redtarg}{ +% \targ[style={draw=red}]{}% +% \setwiretype{n}% +% \wire[l][1]{q} +% } +% \newcommand{\redctrl}[1]{ +% \ctrl[style={draw=red,fill=red,line width=2pt}]{##1} +% } +% \newcommand{\redmeter}{\meter[style={draw=red,fill=red!20}]{}} +% +% \tikzset{ +% noisy/.style={ +% starburst, +% starburst point height=2mm, +% fill=red!25, draw=red!85!black, +% line width=2pt, +% inner xsep=-2pt, inner ysep=-2pt +% }, +% } +% +% \centering +% +% \begin{quantikz}[ +% row sep=4mm, column sep=4mm, +% wire types={q,q,q,q,q,n,n,n,n}, +% execute at end picture={ +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-4-19.north east) +% -- +% (\tikzcdmatrixname-5-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_1$}; +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-6-19.north east) +% -- +% (\tikzcdmatrixname-7-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_2$}; +% \draw [ +% line width=1pt, +% decorate, +% decoration={brace,amplitude=3mm,raise=9mm} +% ] +% (\tikzcdmatrixname-8-19.north east) +% -- +% (\tikzcdmatrixname-9-19.south east) +% node[midway,right,xshift=14mm]{$\text{SE}_3$}; +% } +% ] +% % tex-fmt: off +% & \noise\redwire{18} & \redctrl{3} & & & & & & \redctrl{5} & & & & & & \redctrl{7} & & & & & \\ +% \lstick{$\ket{\psi}$} & \preperr{E_1} & & \ctrl{2} & \ctrl{3} & & & & & \ctrl{4} & \ctrl{5} & & & & & \ctrl{6} & \ctrl{7} & & & \\ +% & \preperr{E_2} & & & & \ctrl{2} & & & & & & \ctrl{4} & & & & & & \ctrl{6} & & \\ +% \lstick{$\ket{0}_{\text{A}_1}$} & & \redtarg{}\redwire{16} & \targ{} & & & & & & & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ +% \lstick{$\ket{0}_{\text{A}_2}$} & & & & \targ{} & \targ{} & & & & & & & & & & & & & \meter{} & \setwiretype{c} \\ +% & & & & & & \lstick{$\ket{0}_{\text{A}_3}$} & \setwiretype{q} & \redtarg\redwire{10} & \targ{} & & & & & & & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ +% & & & & & & \lstick{$\ket{0}_{\text{A}_4}$} & \setwiretype{q} & & & \targ{} & \targ{} & & & & & & & \meter{} & \setwiretype{c} \\ +% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_5}$} & \setwiretype{q} & \redtarg\redwire{4} & \targ{} & & & \redmeter\wire[r][1][style={draw=red,double, line width=2pt}]{q} & \setwiretype{n} \\ +% & & & & & & & & & & & & \lstick{$\ket{0}_{\text{A}_6}$} & \setwiretype{q} & & & \targ{} & \targ{} & \meter{} & \setwiretype{c} +% % tex-fmt: on +% \end{quantikz} +% \end{figure} +% \end{minipage} +% } +% +% \vspace*{8mm} +% +% \addreferencesmanual +% {DTB$^+$25}{ +% P.- J. H. S. Derks et al., ``Designing fault-tolerant +% circuits using detector error models,'' \emph{Quantum}, 2025. +% } +% \stopreferencesmanual +% \end{frame} \begin{frame}[fragile] - \frametitle{The Measurement Syndrome Matrix II} + \frametitle{The Measurement Syndrome Matrix} \vspace*{-18mm} @@ -1909,7 +1909,7 @@ \vspace*{-5mm} \begin{itemize} - \item Pass \ac{cn} to \ac{vn} messages + \item Pass \ac{cn} to \ac{vn} messages to next window \end{itemize} \end{frame} @@ -2927,6 +2927,7 @@ \item \Ac{spa} + \ac{gd} decoder \item Parameters \begin{itemize} + \item $T = 1$ \item $n_\text{iterations} = 32$ \item $F = 1$ \end{itemize}