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Andreas Tsouchlos
2026-05-03 04:26:58 +02:00
parent 6e53ed5d1b
commit dd30b4fc0d
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src/thesis/chapters/4_decoding_under_dems.tex
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@@ -859,10 +859,17 @@ then \ac{bpgd} because of the availability of recently computed messages.
\end{tikzpicture} \end{tikzpicture}
\caption{ \caption{
\red{Visualization of the messages used for the Visualization of the messages carried over from window
initialization of the next window under BP decoding.} $\ell$ to window $\ell + 1$ for the warm-start \ac{bp} inner decoder.
\Acfp{vn} are represented using green circles while \acfp{cn} \Acfp{vn} are represented as green circles, \acfp{cn} as blue squares.
are represented using blue squares. The solid box delimits the nodes of window $\ell$ and the
dashed box those of window $\ell + 1$, with $W$ marking the
window size and $F$ the step size in syndrome rounds.
The \ac{bp} messages on the orange-highlighted edges, which
lie in the overlap region of the two windows, are kept in
memory at the end of the decoding of window $\ell$ and used
to initialize the corresponding messages of window $\ell + 1$
in place of the standard cold-start initialization.
} }
\label{fig:messages_tanner} \label{fig:messages_tanner}
\end{figure} \end{figure}
@@ -1141,11 +1148,20 @@ decimation information after initializing the \ac{cn} to \ac{vn} messages.
\end{tikzpicture} \end{tikzpicture}
\caption{ \caption{
\red{Visualization of the messages and decimation information Visualization of the messages carried over from window
used for the $\ell$ to window $\ell + 1$ for the warm-start \ac{bp} inner decoder.
initialization of the next window under \ac{bpgd} decoding}. \Acfp{vn} are represented as green circles, \acfp{cn} as blue squares.
\Acfp{vn} are represented using green circles while \acfp{cn} The solid box delimits the nodes of window $\ell$ and the
are represented using blue squares. dashed box those of window $\ell + 1$, with $W$ marking the
window size and $F$ the step size in syndrome rounds.
The \ac{bp} messages on the orange-highlighted edges, which
lie in the overlap region of the two windows, are kept in
memory at the end of the decoding of window $\ell$ and used
to initialize the corresponding messages of window $\ell + 1$
in place of the standard cold-start initialization.
In addition to the \ac{bp} messages on the
orange-highlighted edges of the overlap region, decimation
information about the \acp{vn} is also carried over to the next window.
} }
\label{fig:messages_decimation_tanner} \label{fig:messages_decimation_tanner}
\end{figure} \end{figure}
@@ -1333,7 +1349,13 @@ error matrix as a proxy for the attainable decoding performance.
\end{tikzpicture} \end{tikzpicture}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start sliding-window decoding,
compared with whole-block decoding on the full detector error matrix.
The step size is fixed at $F = 1$ and the inner decoder is
min-sum \ac{bp} with at most $200$ iterations.
The underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds under
standard circuit-based depolarizing noise.
} }
\label{fig:whole_vs_cold} \label{fig:whole_vs_cold}
\end{figure} \end{figure}
@@ -1464,7 +1486,14 @@ cold-start curves can be compared directly at matching values of $W$.
\end{tikzpicture} \end{tikzpicture}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding, compared with whole-block decoding on the full
detector error matrix.
The step size is fixed at $F = 1$ and the inner decoder is
min-sum \ac{bp} with at most $200$ iterations.
The underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds under
standard circuit-based depolarizing noise.
} }
\label{fig:whole_vs_cold_vs_warm} \label{fig:whole_vs_cold_vs_warm}
\end{figure} \end{figure}
@@ -1642,7 +1671,17 @@ available to any window.
\end{tikzpicture} \end{tikzpicture}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding as a function of the maximum number of inner \ac{bp}
iterations, compared with whole-block decoding on the full
detector error matrix.
The step size is fixed at $F = 1$, the physical error rate at
$p = 0.0025$, and the iteration budget is swept over
$n_\text{iter} \in \{32, 128, 256, 512, 1024, 2048, 4096\}$.
The inner decoder is min-sum \ac{bp}, the underlying code is
the $\llbracket 144, 12, 12 \rrbracket$ \ac{bb} code over
$12$ syndrome extraction rounds, and the noise model is
standard circuit-based depolarizing noise.
} }
\label{fig:bp_w_over_iter} \label{fig:bp_w_over_iter}
\end{figure} \end{figure}
@@ -1801,8 +1840,8 @@ previous experiments.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the physical error rate at $n_\text{iter}
elit, sed do eiusmod tempor incididunt}} = 200$.}
\label{fig:bp_f_over_p} \label{fig:bp_f_over_p}
\end{subfigure}% \end{subfigure}%
\hfill% \hfill%
@@ -1910,13 +1949,17 @@ previous experiments.
\end{tikzpicture} \end{tikzpicture}
\vspace{-3.2mm} \vspace{-3.2mm}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the num. of iterations at $p = 0.0025$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bp_f_over_iter} \label{fig:bp_f_over_iter}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start
sliding-window decoding at fixed window size $W = 5$.
The inner decoder is min-sum \ac{bp}, the underlying code is
the $\llbracket 144, 12, 12 \rrbracket$ \ac{bb} code over
$12$ syndrome extraction rounds, and the noise model is
standard circuit-based depolarizing noise.
} }
\label{fig:bp_f} \label{fig:bp_f}
\end{figure} \end{figure}
@@ -2107,8 +2150,7 @@ the gain can be achieved even for low values of $T$.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the window size at $F = 1$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_w} \label{fig:bpgd_w}
\end{subfigure}% \end{subfigure}%
\hfill% \hfill%
@@ -2178,13 +2220,22 @@ the gain can be achieved even for low values of $T$.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the step size at $W = 5$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_f} \label{fig:bpgd_f}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding under \ac{bpgd} as a function of the physical error rate.
The warm-start variant carries over both the \ac{bp} messages
and the channel \acp{llr} of the overlap region.
The maximum number of inner \ac{bp} iterations is
$n_\text{iter} = 5000$, chosen to allow nearly every \ac{vn}
in a window to be decimated before the window commits.
The inner \ac{bp} step is implemented using the \ac{spa}, the
underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds, and the
noise model is standard circuit-based depolarizing noise.
} }
\label{fig:bpgd_wf} \label{fig:bpgd_wf}
\end{figure} \end{figure}
@@ -2367,8 +2418,7 @@ fixed physical error rate.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the window size at $F = 1$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_iter_W} \label{fig:bpgd_iter_W}
\end{subfigure}% \end{subfigure}%
\hfill% \hfill%
@@ -2440,13 +2490,21 @@ fixed physical error rate.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the step size at $W = 5$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_iter_F} \label{fig:bpgd_iter_F}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding under \ac{bpgd} as a function of the maximum number
of inner \ac{bp} iterations $n_\text{iter}$.
The warm-start variant carries over both the \ac{bp} messages
and the channel \acp{llr} of the overlap region.
The physical error rate is fixed at $p = 0.0025$.
The inner \ac{bp} step is implemented using the \ac{spa}, the
underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds, and the
noise model is standard circuit-based depolarizing noise.
} }
\label{fig:bpgd_iter} \label{fig:bpgd_iter}
\end{figure} \end{figure}
@@ -2622,8 +2680,7 @@ since the decimation decisions were made based on the messages themselves.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the window size at $F = 1$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_msg_W} \label{fig:bpgd_msg_W}
\end{subfigure}% \end{subfigure}%
\hfill% \hfill%
@@ -2693,13 +2750,21 @@ since the decimation decisions were made based on the messages themselves.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the step size at $W = 5$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_msg_F} \label{fig:bpgd_msg_F}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding under \ac{bpgd} as a function of the physical error rate.
The warm-start variant carries over only the \ac{bp} messages
of the overlap region and not the channel \acp{llr}.
The maximum number of inner \ac{bp} iterations is
$n_\text{iter} = 5000$.
The inner \ac{bp} step is implemented using the \ac{spa}, the
underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds, and the
noise model is standard circuit-based depolarizing noise.
} }
\label{fig:bpgd_msg} \label{fig:bpgd_msg}
\end{figure} \end{figure}
@@ -2830,8 +2895,7 @@ cold-start curves across the entire range of $n_\text{iter}$ available to us.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the window size at $F = 1$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_msg_iter_W} \label{fig:bpgd_msg_iter_W}
\end{subfigure}% \end{subfigure}%
\hfill% \hfill%
@@ -2903,13 +2967,21 @@ cold-start curves across the entire range of $n_\text{iter}$ available to us.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing \caption{Sweep over the step size at $W = 5$.}
elit, sed do eiusmod tempor incididunt}}
\label{fig:bpgd_msg_iter_F} \label{fig:bpgd_msg_iter_F}
\end{subfigure} \end{subfigure}
\caption{ \caption{
\red{\lipsum[2]} Per-round \ac{ler} of cold-start and warm-start sliding-window
decoding under \ac{bpgd} as a function of the maximum number
of inner \ac{bp} iterations $n_\text{iter}$, where the
warm-start variant carries over only the \ac{bp} messages of
the overlap region and not the channel \acp{llr}.
The physical error rate is fixed at $p = 0.0025$.
The inner \ac{bp} step is implemented using the \ac{spa}, the
underlying code is the $\llbracket 144, 12, 12 \rrbracket$
\ac{bb} code over $12$ syndrome extraction rounds, and the
noise model is standard circuit-based depolarizing noise.
} }
\label{fig:bpgd_msg_iter} \label{fig:bpgd_msg_iter}
\end{figure} \end{figure}