Add paragraphs exp. params, description, and interpretation for fig. 4.9

src/thesis/chapters/4_decoding_under_dems.tex

@@ -1476,23 +1476,6 @@ irrespective of the initialization, can beat, since by construction
 whole-block decoding has access to the full set of constraints
 available to any window.
 
-% [Description] Figure 4.9
-%   - Parameters
-%     - # BP iterations
-%     - W,F
-%     - Physical error rates
-%     - Warm vs cold start
-%   - Figure description
-%     - TODO:
-
-% [Interpretation] Figure 4.9
-%   -
-
-% At some later point
-\content{When looking at max iterations: Callback to diminishing
-    returns with growing window size: More iterations more beneficial
-than larger window (+1 for warm-start)}
-
 \begin{figure}[t]
     \centering
     \begin{tikzpicture}
@@ -1598,104 +1581,86 @@ than larger window (+1 for warm-start)}
     \caption{
         \red{\lipsum[2]}
     }
+    \label{fig:bp_w_over_iter}
 \end{figure}
 
-% \begin{figure}[t]
+% [Experimental parameters] Figure 4.9
-%     \centering
+
-%     \begin{tikzpicture}[spy using outlines={circle, magnification=2,
+\Cref{fig:bp_w_over_iter} shows the per-round \ac{ler} as a function
-%         connect spies}]
+of the maximum number of \ac{bp} iterations granted to the inner decoders.
-%
+The dashed colored curves correspond to cold-start sliding-window
-%         \begin{axis}[
+decoding for $W \in \{3, 4, 5\}$, the solid colored curves to the
-%                 width=\figwidth,
+corresponding warm-start sliding-window decoding, and the black curve
-%                 height=\figheight,
+to the whole-block reference.
-%                 ymode=log,
+The physical error rate is fixed at $p = 0.0025$, the step size at
-%                 % xmode=log,
+$F = 1$, and the iteration budget is swept over
-%                 legend style={
+$n_\text{iter} \in \{32, 128, 256, 512, 1024, 2048, 4096\}$.
-%                     cells={anchor=west},
+The enlarged plot magnifies the low-iteration regime
-%                     cells={align=left},
+$n_\text{iter} \in [32, 512]$.
-%                 },
+
-%                 enlargelimits=false,
+% [Description] Figure 4.9
-%                 ymin=1e-3, ymax=1e-1,
+
-%                 grid=both,
+All curves decrease monotonically with the iteration budget, but
-%                 legend pos = north east,
+contrary to our expectation, none of them appears to fully saturate
-%                 xtick={32,512,1024,2048,4096},
+within the swept range: even at $n_\text{iter} = 4096$, every curve
-%                 % xtick={0.001,0.0015,...,0.004},
+still exhibits a noticeable downward slope.
-%                 xticklabels =
+At $n_\text{iter} = 32$, the whole-block curve lies below both the
-%                 {$32$,$512$,$1{,}024$,,$2{,}048$,,$3{,}072$,,$4{,}096$},
+$W=4$ and $W=5$ sliding-window curves.
-%                 xtick={32, 512, 1024, 1536, 2048, 2560, 3072, 3584, 4096},
+At $n_\text{iter} = 128$ the whole-block curve already performs
-%                 xticklabel style={/pgf/number format/fixed},
+better than the $W=4$ sliding-window curve
-%                 xticklabel style={/pgf/number format/precision=4},
+and at $n_\text{iter} = 512$ the whole-block and warm-start $W = 5$
-%                 % x tick label style={rotate=45, anchor=north east,
+curves also cross.
-%                 % inner sep=1mm},
+From this point onwards, the whole-block decoder lies strictly below
-%                 scaled x ticks=false,
+all windowed schemes, this difference becoming more pronounced as the
-%                 xlabel={Number of BP iterations},
+iteration budget grows further.
-%                 ylabel={Per-round-LER},
+Within the magnified plot, the gap between the warm-start and
-%                 extra description/.code={
+cold-start curves at fixed $W$ is largest for the smallest iteration
-%                     \node[rotate=90, anchor=south]
+counts and shrinks rapidly as $n_\text{iter}$ grows, and at fixed
-%                     at ([xshift=10mm]current axis.east)
+$n_\text{iter}$ the size of this gap grows with the window size,
-%                     {Warm s. (---), Cold s. (- - -)};
+mirroring the behavior already observed in \Cref{fig:whole_vs_cold_vs_warm}.
-%                 },
+
-%             ]
+% [Interpretation] Figure 4.9
-%
+
-%             \foreach \W/\col/\mark in
+These observations are largely consistent with the effective-iterations
-%             {3/KITred/triangle,4/KITblue/diamond,5/KITorange/square} {
+hypothesis put forward above.
-%                 \edef\temp{\noexpand
+The whole-block decoder eventually overtaking every windowed scheme
-%                     \addplot+[mark=\mark, densely dashed,
+matches the prediction made there: with a sufficiently large
-%                     forget plot, \col]
+iteration budget, the whole-block decoder reaches an error rate
-%                     table[
+that nonone of the windowed schemes can beat, because of the more global
-%                         col sep=comma, x=max_iter,
+nature of the considered constraints.
-%                         y=LER_per_round,
+Furthermore, the pronounced advantage of warm- over cold-start decoding at low
-%                     ]
+numbers of iterations makes sense if we consider the overall trend of the plots.
-%                     {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_False/F_1/W_\W/LERs.csv};
+At low iteration budgets, each additional iteration is worth more
-%                 }
+than at high budgets.
-%                 \temp
+As the number of permitted iteration increases, the benefit of
-%             }
+the additional ``free'' iterations gained due to the the warm-start
-%
+initialization diminishes, and the curves approach each other.
-%             \foreach \W/\col/\mark in
+
-%             {3/KITred/triangle*,4/KITblue/diamond*,5/KITorange/square*} {
+The fact that no curve clearly saturates within the swept range is
-%                 \edef\temp{\noexpand
+itself worth noting.
-%                     \addplot+[mark=\mark, solid, mark
+We know that \ac{bp} on \ac{qldpc} codes suffers from poor
-%                     options={fill=\col}, \col]
+convergence due to the short cycles in the underlying Tanner graph,
-%                     table[
+so even after several thousand iterations the
-%                         col sep=comma, x=max_iter,
+decoder may continue to slowly refine its message estimates rather
-%                         y=LER_per_round,
+than settle into a stable fixed point.
-%                     ]
+This is one of the core motivations for moving from plain \ac{bp} to
-%                     {res/sim/max_iter/WindowingSyndromeMinSumDecoder/p_0.0025/pass_soft_info_True/F_1/W_\W/LERs.csv};
+the guided-decimation variant studied in
-%                 }
+\Cref{subsec:Belief Propagation with Guided Decimation}.
-%                 \temp
+
-%
+Another thing to note is that setting the per-invocation iteration
-%                 \addlegendentryexpanded{$W = \W$}
+budget of the inner decoder equal to the iteration budget of the
-%             }
+whole-block decoder is not a fair comparison in terms of total
-%
+computational effort.
-%             \addplot+[mark=*, solid, mark options={fill=black}, black]
+The sliding-window scheme processes each \ac{vn} in an overlap region
-%             table[
+multiple times and therefore spends more iterations overall.
-%                 col sep=comma, x=max_iter,
+In the context of \ac{qec}, however, the relevant figure of merit is
-%                 y=LER_per_round,
+not total compute but decoding latency, and in terms of latency the
-%             ]
+sliding-window approach is still at an advantage.
-%             {res/sim/max_iter/SyndromeMinSumDecoder/p_0.0025/LERs.csv};
+
-%
+% At some later point
-%             \addlegendentry{Whole}
+\content{When looking at max iterations: Callback to diminishing
-%
+    returns with growing window size: More iterations more beneficial
-%             \coordinate (spypoint) at (axis cs:250,1e-2);
+than larger window (+1 for warm-start)}
-%             \coordinate (magnifyglass) at (axis cs:2048,0.5);
-%
-%         \end{axis}
-%         \spy [black, size=4cm] on (spypoint)
-%         in node[fill=white] at (magnifyglass);
-%
-%     \end{tikzpicture}
-%
-%     \caption{
-%         Comparison of the decoding performance of cold and warm-start
-%         decoding under the $\llbracket 144,12,12 \rrbracket$ \ac{bb}
-%         code for different step sizes.
-%         Decoding was performed using the min-sum algorithm ($200$
-%         iterations).
-%         The window size was fixed to $W=5$, $12$ rounds of syndrome
-%         extraction were performed and the noise model is
-%         standard circuit-based depolarizing noise.
-%     }
-% \end{figure}
 
 \begin{figure}[t]
     \centering

src/thesis/chapters/5_conclusion_and_outlook.tex

@@ -1,8 +1,11 @@
 \chapter{Conclusion and Outlook}
 
+\content{Takeaway: Warm-start more effective for lower numbers of max
+    iterations (plays into our hands because lower number of iterations
+means lower latency)}
+
 \content{\textbf{Ideas for further research}}
 \content{Softer way of decimating VNs}
 \content{Systematic study on using different inner decoders (AED,
 SED, BPGD, ...)}
 \content{Investigate SC-LDPC window decoding wave-like effects}
-