diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex
index ffc91ee..dcc098e 100644
--- a/src/thesis/chapters/4_decoding_under_dems.tex
+++ b/src/thesis/chapters/4_decoding_under_dems.tex
@@ -1801,7 +1801,8 @@ previous experiments.
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of window sizes for $F=1$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
         \label{fig:bp_f_over_p}
     \end{subfigure}%
     \hfill%
@@ -1909,7 +1910,8 @@ previous experiments.
         \end{tikzpicture}
         \vspace{-3.2mm}
 
-        \caption{Comparison of step sizes for $W=5$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
         \label{fig:bp_f_over_iter}
     \end{subfigure}
 
@@ -2025,6 +2027,15 @@ This motivates the next subsection, in which we replace the inner
 \subsection{Belief Propagation with Guided Decimation}
 \label{subsec:Belief Propagation with Guided Decimation}
 
+% [Thread] Intro to BPGD + Local experimental setup
+
+We now turn to \ac{bpgd} as the inner decoder, in order to address
+the convergence issues of plain \ac{bp} on \ac{qec} codes.
+For the underlying \ac{bp} step we use the \ac{spa} variant rather
+than the min-sum approximation employed in
+\Cref{subsec:Belief Propagation}, since this made the implementation
+of the guided decimation more straightforward.
+
 \begin{figure}[t]
     \centering
     \hspace*{-6mm}
@@ -2053,7 +2064,7 @@ This motivates the next subsection, in which we replace the inner
                     ylabel={Per-round-LER},
                     % extra description/.code={
                     %     \node[rotate=90, anchor=south]
-                    %     at ([xshift=10mm]current axis.east)
+                    %     at ()
                     %     {Warm s. (---), Cold s. (- - -)};
                     % },
                 ]
@@ -2093,7 +2104,9 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of window sizes for $F=1$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
+        \label{fig:bpgd_w}
     \end{subfigure}%
     \hfill%
     \begin{subfigure}{0.5\textwidth}
@@ -2162,14 +2175,112 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of step sizes for $W=5$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
+        \label{fig:bpgd_f}
     \end{subfigure}
 
     \caption{
         \red{\lipsum[2]}
     }
+    \label{fig:bpgd_wf}
 \end{figure}
 
+% [Experimental parameters] Figure 4.10
+
+\Cref{fig:bpgd_wf} shows the per-round \ac{ler} of \ac{bpgd}
+sliding-window decoding as a function of the physical error rate.
+In both panels the dashed curves correspond to cold-start
+sliding-window decoding and the solid curves to the
+corresponding warm-start decoding, where the warm start carries over both
+the \ac{bp} messages and the decimation information of the overlap
+region as described in
+\Cref{subsec:Warm-Start Belief Propagation with Guided Decimation Decoding}.
+The maximum number of inner \ac{bp} iterations was set to
+$n_\text{iter} = 5000$.
+This value was chosen to be at least as large as the number of
+\acp{vn} in any single window, since with one \ac{bp} iteration
+between consecutive decimations ($T = 1$ in the notation of
+\Cref{alg:bpgd}) this is the maximum number of inner iterations
+that can occur before every \ac{vn} in the window has been decimated.
+A preliminary investigation showed that \ac{bpgd} only delivers its
+intended performance gain once most \acp{vn} have actually been decimated,
+which motivated this choice.
+The physical error rate was swept from $p = 0.001$ to $p = 0.004$
+in steps of $0.0005$.
+\Cref{fig:bpgd_w} sweeps over the window size with
+$W \in \{3, 4, 5\}$ at fixed step size $F = 1$, and
+\Cref{fig:bpgd_f} sweeps over the step size with
+$F \in \{1, 2, 3\}$ at fixed window size $W = 5$.
+
+% [Description] Figure 4.10
+
+In both panels, every curve again exhibits the expected monotonic
+increase of the per-round \ac{ler} with the physical error rate.
+Across both panels and across all parameter choices, the warm-start
+curves lie above the corresponding cold-start curves, i.e.,
+the warm-start variant performsworse than its cold-start counterpart.
+This is the opposite of what we observed for plain \ac{bp}, where
+warm-start improved upon cold-start at every parameter setting.
+The gap between the warm- and cold-start curves additionally widens
+as the physical error rate decreases:
+at the lowest sampled rate $p = 0.001$, the per-round \ac{ler} of the
+warm-start runs is more than two orders of magnitude above that of
+the corresponding cold-start runs.
+In \Cref{fig:bpgd_w}, larger window sizes yield lower per-round
+\acp{ler} for both warm- and cold-start, and the spacing between the
+cold-start curves shrinks as $W$ grows.
+In \Cref{fig:bpgd_f}, the cold-start curves follow the previously seen
+ordering with $F = 1$ at the bottom and $F = 3$ at the top.
+The warm-start curves, however, exhibit the opposite ordering:
+$F = 1$ now yields the highest per-round \ac{ler}, $F = 2$ lies below
+it, and $F = 3$ is the lowest of the three warm-start curves.
+
+% [Interpretation] Figure 4.10
+
+The fact that warm-start sliding-window decoding now performs worse
+than its cold-start counterpart is surprising in light of the results
+for plain \ac{bp}, where the warm-start modification was uniformly beneficial.
+The dependence on the window size in \Cref{fig:bpgd_w} is, on its own,
+consistent with the same explanation that we gave for
+\Cref{fig:whole_vs_cold}: larger windows expose the inner decoder to
+a larger fraction of the constraints encoded in the detector error
+matrix at the time of decoding, and this benefits both warm- and
+cold-start decoding.
+The dependence on the step size in \Cref{fig:bpgd_f}, however, is the
+opposite of the corresponding dependence under plain \ac{bp}
+(\Cref{fig:bp_f_over_p}): for warm-start, smaller $F$ now hurts
+rather than helps, even though smaller $F$ implies a larger overlap
+in both cases.
+
+This inversion provides the clue to what is going wrong.
+Recall from
+\Cref{subsec:Warm-Start Belief Propagation with Guided Decimation Decoding}
+that the warm start for \ac{bpgd} carries over not only the \ac{bp}
+messages on the edges of the overlap region but also the decimation
+information.
+Because we run with an iteration budget large enough to decimate
+every \ac{vn} in a window, by the time window $\ell$ ends, all
+of its \acp{vn} have already been hard-decided.
+For the \acp{vn} that lie in the overlap region with window $\ell + 1$
+this hard decision is then carried into the next window through the
+warm-start initialization, and the next window thus begins decoding
+with a substantial fraction of its \acp{vn} already frozen, before
+its own parity checks have had any chance to influence the
+corresponding bit estimates.
+This identifies one of two competing effects on the warm-start performance.
+The larger the overlap, the more such prematurely frozen \acp{vn} the
+next window inherits, which hurts performance.
+On the other hand, a larger window still exposes the inner decoder to
+a larger set of constraints, which helps performance.
+The two effects together are consistent with what we observe in
+\Cref{fig:bpgd_wf}.
+Increasing $W$ at fixed $F$ enlarges both the overlap and the window
+itself, and the benefit due to the larger $W$ dominates.
+Decreasing $F$ at fixed $W$, by contrast, enlarges only the overlap
+without enlarging the window, so the freezing effect is no longer
+offset and warm-start performance worsens with smaller $F$.
+
 \begin{figure}[t]
     \centering
     \hspace*{-6mm}
@@ -2240,7 +2351,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of window sizes for $F=1$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}%
     \hfill%
     \begin{subfigure}{0.48\textwidth}
@@ -2311,9 +2423,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{
-            Comparison of step sizes for $W=5$.
-        }
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}
 
     \caption{
@@ -2389,7 +2500,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of window sizes for $F=1$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}%
     \hfill%
     \begin{subfigure}{0.5\textwidth}
@@ -2458,7 +2570,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of step sizes for $W=5$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}
 
     \caption{
@@ -2536,7 +2649,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{Comparison of window sizes for $F=1$.}
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}%
     \hfill%
     \begin{subfigure}{0.48\textwidth}
@@ -2607,9 +2721,8 @@ This motivates the next subsection, in which we replace the inner
             \end{axis}
         \end{tikzpicture}
 
-        \caption{
-            Comparison of step sizes for $W=5$.
-        }
+        \caption{\red{Lorem ipsum dolor sit amet, consectetur adipiscing
+        elit, sed do eiusmod tempor incididunt}}
     \end{subfigure}
 
     \caption{