From dd30b4fc0dc82364e06c76ac34e3776b975b9103 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sun, 3 May 2026 04:26:58 +0200 Subject: [PATCH] Write captions --- src/thesis/chapters/4_decoding_under_dems.tex | 146 +++++++++++++----- 1 file changed, 109 insertions(+), 37 deletions(-) diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex index 58eb116..16d487a 100644 --- a/src/thesis/chapters/4_decoding_under_dems.tex +++ b/src/thesis/chapters/4_decoding_under_dems.tex @@ -859,10 +859,17 @@ then \ac{bpgd} because of the availability of recently computed messages. \end{tikzpicture} \caption{ - \red{Visualization of the messages used for the - initialization of the next window under BP decoding.} - \Acfp{vn} are represented using green circles while \acfp{cn} - are represented using blue squares. + Visualization of the messages carried over from window + $\ell$ to window $\ell + 1$ for the warm-start \ac{bp} inner decoder. + \Acfp{vn} are represented as green circles, \acfp{cn} as 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} \end{figure} @@ -1141,11 +1148,20 @@ decimation information after initializing the \ac{cn} to \ac{vn} messages. \end{tikzpicture} \caption{ - \red{Visualization of the messages and decimation information - used for the - initialization of the next window under \ac{bpgd} decoding}. - \Acfp{vn} are represented using green circles while \acfp{cn} - are represented using blue squares. + Visualization of the messages carried over from window + $\ell$ to window $\ell + 1$ for the warm-start \ac{bp} inner decoder. + \Acfp{vn} are represented as green circles, \acfp{cn} as 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. + 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} \end{figure} @@ -1333,7 +1349,13 @@ error matrix as a proxy for the attainable decoding performance. \end{tikzpicture} \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} \end{figure} @@ -1464,7 +1486,14 @@ cold-start curves can be compared directly at matching values of $W$. \end{tikzpicture} \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} \end{figure} @@ -1642,7 +1671,17 @@ available to any window. \end{tikzpicture} \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} \end{figure} @@ -1801,8 +1840,8 @@ previous experiments. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the physical error rate at $n_\text{iter} + = 200$.} \label{fig:bp_f_over_p} \end{subfigure}% \hfill% @@ -1910,13 +1949,17 @@ previous experiments. \end{tikzpicture} \vspace{-3.2mm} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the num. of iterations at $p = 0.0025$.} \label{fig:bp_f_over_iter} \end{subfigure} \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} \end{figure} @@ -2107,8 +2150,7 @@ the gain can be achieved even for low values of $T$. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the window size at $F = 1$.} \label{fig:bpgd_w} \end{subfigure}% \hfill% @@ -2178,13 +2220,22 @@ the gain can be achieved even for low values of $T$. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the step size at $W = 5$.} \label{fig:bpgd_f} \end{subfigure} \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} \end{figure} @@ -2367,8 +2418,7 @@ fixed physical error rate. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the window size at $F = 1$.} \label{fig:bpgd_iter_W} \end{subfigure}% \hfill% @@ -2440,13 +2490,21 @@ fixed physical error rate. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the step size at $W = 5$.} \label{fig:bpgd_iter_F} \end{subfigure} \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} \end{figure} @@ -2622,8 +2680,7 @@ since the decimation decisions were made based on the messages themselves. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the window size at $F = 1$.} \label{fig:bpgd_msg_W} \end{subfigure}% \hfill% @@ -2693,13 +2750,21 @@ since the decimation decisions were made based on the messages themselves. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the step size at $W = 5$.} \label{fig:bpgd_msg_F} \end{subfigure} \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} \end{figure} @@ -2830,8 +2895,7 @@ cold-start curves across the entire range of $n_\text{iter}$ available to us. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the window size at $F = 1$.} \label{fig:bpgd_msg_iter_W} \end{subfigure}% \hfill% @@ -2903,13 +2967,21 @@ cold-start curves across the entire range of $n_\text{iter}$ available to us. \end{axis} \end{tikzpicture} - \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing - elit, sed do eiusmod tempor incididunt}} + \caption{Sweep over the step size at $W = 5$.} \label{fig:bpgd_msg_iter_F} \end{subfigure} \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} \end{figure}