diff --git a/src/thesis/chapters/4_decoding_under_dems.tex b/src/thesis/chapters/4_decoding_under_dems.tex
index 200cdfa..2b99789 100644
--- a/src/thesis/chapters/4_decoding_under_dems.tex
+++ b/src/thesis/chapters/4_decoding_under_dems.tex
@@ -512,6 +512,9 @@ $\mathcal{J}_\text{win}^{(\ell)}$ is the set of all \acp{cn} in the
 window while $\mathcal{J}_\text{commit}^{(\ell)}$ is the set of \acp{cn}
 that do not contribute to the next window and whose neighboring
 \acp{vn} will thus be comitted.
+We can additionally define the set of \acp{vn} that are shared between windows
+$\ell$ and $\ell + 1$ as $\mathcal{J}_\text{overlap}^{(\ell)} :=
+\mathcal{J}_\text{win}^{(\ell)}\setminus \mathcal{J}_\text{commit}^{(\ell)}$.
 
 % How we get the corresponding columns
 
@@ -563,6 +566,76 @@ Note that we have
 \end{align*}
 and after decoding all windows we will therefore have committed all \acp{vn}.
 
+\begin{figure}[t]
+    \centering
+
+    \begin{tikzpicture}
+        \def\sx{1.5}
+        \def\sy{1.5}
+
+        \coordinate (a00) at (0,0);
+        \coordinate (a01) at (0,      3*\sy);
+        \coordinate (a11) at (6*\sx,  3*\sy);
+        \coordinate (a10) at (6*\sx,  0*\sy);
+
+        \coordinate (b00) at (3.2*\sx, -1*\sy);
+        \coordinate (b01) at (3.2*\sx,  2*\sy);
+        \coordinate (b11) at (9.2*\sx,  2*\sy);
+        \coordinate (b10) at (9.2*\sx, -1*\sy);
+
+        \fill[gray!40] (a00) -- (a00 |- b01) -- (b01) -- (b01 |- a00) -- cycle;
+
+        \draw (a00) -- (a01) -- (a11) -- (a10) -- cycle;
+        \draw[densely dashed] (b00) -- (b01) -- (b11) -- (b10) -- cycle;
+
+        \draw [
+            decorate,
+            decoration={brace,amplitude=3mm,raise=1mm}
+        ]
+        (a01) -- (a11)
+        node[midway,above,yshift=4mm]{$\mathcal{I}_\text{win}^{(\ell)}$};
+
+        \draw [
+            decorate,
+            decoration={brace,amplitude=3mm,raise=1mm}
+        ]
+        (a00 -| b00) -- (a00)
+        node[midway,below,yshift=-4mm]{$\mathcal{I}_\text{commit}^{(\ell)}$};
+
+        \draw [
+            decorate,
+            decoration={brace,amplitude=3mm,raise=1mm}
+        ]
+        (a00) -- (a01)
+        node[midway,xshift=-3mm,left]{$\mathcal{J}_\text{win}^{(\ell)}$};
+
+        \draw [
+            decorate,
+            decoration={brace,amplitude=3mm,raise=1mm}
+        ]
+        (a11) -- (a11 |- b11)
+        node[midway,xshift=3mm,right]{$\mathcal{J}_\text{commit}^{(\ell)}$};
+
+        \draw [
+            decorate,
+            decoration={brace,amplitude=3mm,raise=1mm}
+        ]
+        (a11 |- b11) -- (a10)
+        node[midway,xshift=3mm,right]{$\mathcal{J}_\text{overlap}^{(\ell)}
+            := \mathcal{J}_\text{win}^{(\ell)} \setminus
+        \mathcal{J}_\text{commit}^{(\ell)}$};
+
+        \node at ($(a00)!0.5!(b01)$)
+        {$\left(\bm{H}_\text{DEM}\right)_{\mathcal{J}_\text{overlap}^{(\ell)},
+        \mathcal{I}_\text{commit}^{(\ell)}}$};
+    \end{tikzpicture}
+
+    \caption{Visual representation of notation for window splitting.}
+    \label{fig:vis_rep}
+\end{figure}
+
+\Cref{fig:vis_rep} illustrates the meaning of the various sets of nodes.
+
 % Syndrome update
 
 \content{Why we need to update the syndrome}
@@ -578,7 +651,6 @@ and after decoding all windows we will therefore have committed all \acp{vn}.
 \content{4. Decode next window}
 \content{(?) Explicitly mention we don't reuse existing messages?}
 
-\content{Definition for last window is different}
 \content{Double-check all definitions}
 
 % TODO: Do I need this?