diff --git a/src/final_presentation/main.tex b/src/final_presentation/main.tex index b79d02d..c9d8b1e 100644 --- a/src/final_presentation/main.tex +++ b/src/final_presentation/main.tex @@ -1882,6 +1882,11 @@ \vspace*{-18mm} + % Idea for why lower error rate -> larger improvement + % - Lower error rate + % -> soft info more accurate earlier + % -> passed info worth more + \begin{itemize} \item Examine decoding performance for \schlagwort{BP} \item Larger improvement for lower error rate @@ -2485,6 +2490,10 @@ \begin{minipage}{0.33\textwidth} \centering \begin{itemize} + \vspace*{-20mm} + \item Smaller step size\\ + $\implies$ More overlap + \vspace*{10mm} \item $\llbracket 144,12,12\rrbracket$ \ac{bb} code \item $12$ \ac{se} rounds \item Min-sum decoder @@ -2617,6 +2626,10 @@ \begin{minipage}{0.33\textwidth} \centering \begin{itemize} + \vspace*{-20mm} + \item Smaller step size\\ + $\implies$ More overlap + \vspace*{10mm} \item $\llbracket 144,12,12\rrbracket$ \ac{bb} code \item $12$ \ac{se} rounds \item Min-sum decoder @@ -2749,6 +2762,10 @@ \begin{minipage}{0.33\textwidth} \centering \begin{itemize} + \vspace*{-20mm} + \item Smaller step size\\ + $\implies$ More overlap + \vspace*{10mm} \item $\llbracket 144,12,12\rrbracket$ \ac{bb} code \item $12$ \ac{se} rounds \item Min-sum decoder @@ -2769,20 +2786,23 @@ \vspace*{-10mm} \centering \begin{itemize} - \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} + \item Most error due to non-convergence \vspace*{10mm} - \item Mitigates problems due to degeneracy \\ - $\implies$ Decoder is encouraged to focus on \\ - \hspace{9mm} one solution + \visible<2-> { + \item BPGD algorithm \citereferencemanual{YLH+24} + \begin{enumerate} + \item Perform $T$ \schlagwort{BP iterations} + \item Hard decision on \schlagwort{most reliable \ac{vn}} + \item \schlagwort{Exclude \ac{vn}} from further processing + \item Go back to step 1 + \end{enumerate} + \vspace*{10mm} + \item Mitigates convergence problems + } \end{itemize} \end{minipage}% \begin{minipage}{0.5\textwidth} - \visible<2->{ + \visible<3->{ \centering \vspace*{-10mm} @@ -3681,114 +3701,6 @@ \end{minipage} \end{frame} -% \begin{frame} -% \frametitle{Summary} -% -% \begin{minipage}{0.66\textwidth} -% \centering -% \begin{figure}[H] -% \centering -% \begin{tikzpicture} -% \begin{axis}[ -% width=16cm, -% height=12cm, -% ymode=log, -% legend style={ -% cells={anchor=west}, -% cells={align=left}, -% }, -% enlargelimits=false, -% ymin=1e-5, ymax=2e-1, -% grid=both, -% legend pos = south east, -% xtick={0.001,0.0015,...,0.004}, -% xticklabel style={/pgf/number format/fixed}, -% xticklabel style={/pgf/number format/precision=4}, -% scaled x ticks=false, -% xlabel={Physical error rate}, -% ylabel={Per-round-LER}, -% extra description/.code={ -% \node[rotate=90, anchor=south] -% at ([xshift=15mm]current axis.east) -% {Warm s. (---), Cold s. (- - -)}; -% }, -% ] -% -% \foreach \F/\col in -% {3/kit-red,2/kit-blue,1/kit-orange} { -% \edef\temp{\noexpand -% \addplot+[mark=o, line width=2pt, -% forget plot, solid, gray, opacity=0.35] -% table[ -% col sep=comma, x=physical_p, -% y=LER_per_round, -% ] -% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_200/pass_soft_info_True/F_\F/W_5/LERs.csv}; -% } -% \temp -% -% \edef\temp{\noexpand -% \addplot+[mark=o, line width=2pt, -% forget plot, densely dashed, gray, -% opacity=0.35] -% table[ -% col sep=comma, x=physical_p, -% y=LER_per_round, -% ] -% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_200/pass_soft_info_False/F_\F/W_5/LERs.csv}; -% } -% \temp -% } -% -% \foreach \F/\col in -% {3/kit-red,2/kit-blue,1/kit-orange} { -% \edef\temp{\noexpand -% \addplot+[mark=o, line width=2pt, -% solid, \col] -% table[ -% col sep=comma, x=physical_p, -% y=LER_per_round, -% ] -% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_5000/pass_soft_info_True/F_\F/W_5/LERs.csv}; -% } -% \temp -% -% \addlegendentryexpanded{$F = \F$} -% } -% -% \foreach \F/\col in -% {3/kit-red,2/kit-blue,1/kit-orange} { -% \edef\temp{\noexpand -% \addplot+[mark=o, line width=2pt, -% densely dashed, \col] -% table[ -% col sep=comma, x=physical_p, -% y=LER_per_round, -% ] -% {res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_5000/pass_soft_info_False/F_\F/W_5/LERs.csv}; -% } -% \temp -% } -% \end{axis} -% \end{tikzpicture} -% \end{figure} -% \end{minipage}% -% \begin{minipage}{0.33\textwidth} -% \centering -% \begin{itemize} -% \item $\llbracket 144,12,12\rrbracket$ \ac{bb} code, \\ -% $12$ \ac{se} rounds -% \item \ac{spa} + \ac{gd} decoder -% \item Parameters -% \begin{itemize} -% \item $T = 1$ -% \item $n_\text{iterations} = 5000$ -% \item $W = 5$ -% \end{itemize} -% \end{itemize} -% \end{minipage} -% \end{frame} - \begin{frame} \frametitle{BPGD: Passing Decimation Information} @@ -3883,58 +3795,6 @@ \end{minipage} \end{frame} -% \begin{frame} -% \frametitle{Future Work} -% -% \vspace*{-15mm} -% -% \begin{itemize} -% \item Completed work -% \begin{itemize} -% \item Review literature on fault-tolerant \ac{qec} -% using \acp{dem} -% \item Identify research gap -% \item Familiarize with software toolboxes -% \end{itemize} -% \vspace*{7mm} -% \item Research gap -% \begin{itemize} -% \item Existing literature into circuit-level noise -% fails to properly consider \ac{scldpc}-like -% structure -% \end{itemize} -% \vspace*{7mm} -% \visible<2->{ -% \item Future directions -% \begin{itemize} -% \item Adapt modified guided decimation decoder from -% \citereferencemanual{GCR24} to pass soft -% information -% \item Investigate performance of different -% modifications of \ac{bp} for "inner decoder" -% (e.g., quaternary neural \ac{bp} -% \citereferencemanual{MSL$^+$25}) -% \item \ldots -% \end{itemize} -% } -% \end{itemize} -% -% \vspace*{10mm} -% -% \addreferencesmanual -% {GCR24}{ -% A. Gong, S. Cammerer, and J. M. Renes, ``Toward -% Low-latency Iterative Decoding of QLDPC Codes Under -% Circuit-Level Noise,'' 2024. -% } -% {MSL$^+$25}{ -% S. Miao et al., ``Quaternary neural belief propagation -% decoding of quantum LDPC codes with overcomplete -% check matrices'', \emph{IEEE Access}, 2025. -% } -% \stopreferencesmanual -% \end{frame} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion and Outlook} \label{subsec:Conclusion and Outlook}