Added average error figure and changed figure positioning to h

latex/thesis/chapters/proximal_decoding.tex

@@ -357,7 +357,7 @@ using a \ac{BP} decoder, as a reference.
 The results from Wadayama et al. are shown with solid lines,
 while the newly generated ones are shown with dashed lines.
 
-\begin{figure}[H]
+\begin{figure}[h]
     \centering
 
     \begin{tikzpicture}
@@ -434,12 +434,11 @@ Evidently, while the decoding performance does depend on the value of
 $\gamma$, there is no single optimal value offering optimal performance, but
 rather a certain interval in which it stays largely unchanged.
 When examining a number of different codes (figure
-\ref{fig:prox:results_3d_multiple}), \todo{Move figure to appendix?}
-it is apparent that while the exact
+\ref{fig:prox:results_3d_multiple}), it is apparent that while the exact
 landscape of the graph depends on the code, the general behaviour is the same
 in each case.
 
-\begin{figure}[H]
+\begin{figure}[h]
     \centering
 
     \begin{tikzpicture}
@@ -509,7 +508,7 @@ similar values of the two step sizes.
 Again, this consideration applies to a multitude of different codes, as
 depicted in figure \ref{fig:prox:gamma_omega_multiple}.
 
-\begin{figure}[H]
+\begin{figure}[h]
     \centering
 
     \begin{tikzpicture}
@@ -528,7 +527,7 @@ depicted in figure \ref{fig:prox:gamma_omega_multiple}.
             point meta min=-5.7,
             point meta max=-0.5,
             colorbar style={
-                title={$E_b / N_0$},
+                title={\acs{BER}},
                 ytick={-5,-4,...,-1},
                 yticklabels={$10^{-5}$,$10^{-4}$,$10^{-3}$,$10^{-2}$,$10^{-1}$}
             }]
@@ -558,18 +557,60 @@ the average error is inspected.
 This time $\gamma$ and $\omega$ are held constant and the average error is
 observed during each iteration of the decoding process for a number of
 different \acp{SNR}.
-The plots have been generated by averaging the error over TODO decodings.
+The plots have been generated by averaging the error over $\SI{500000}{}$ decodings.
 As some decodings go one for more iterations than others, the number of values
 which are averaged for each datapoints vary.
-This explains the bump visible around $k=\text{TODO}$, since after
-this point more and more correct decodings converge and stop iterating,
+This explains the dip visible in all curves around $k=20$, since after
+this point more and more correct decodings stop iterating,
 leaving more and more faulty ones to be averaged.
+A this point the decline in the average error stagnates, rendering an
+increase in $K$ counterproductive as it only raises the average timing
+requirements of the decoding process.
+The higher the \ac{SNR}, the fewer decodings are present at each iteration
+to average, since a solution is found earlier.
+This explains the decreasing smootheness of the lines as the \ac{SNR} rises.
 Remarkably, the \ac{SNR} seems to not have any impact on the number of
 iterations necessary to reach the point at which the average error
 stabilizes.
-Furthermore, the improvement in decoding performance stagnates at a particular
-point, rendering an increase in $K$ counterproductive as it only raises the
-average timing requirements of the decoding process.
+
+\begin{figure}[h]
+    \centering
+
+    \begin{tikzpicture}
+        \begin{axis}[
+            grid=both,
+            xlabel={Iterations},
+            ylabel={Average $\lVert \boldsymbol{c}-\boldsymbol{\hat{c}} \rVert$},
+            legend pos=outer north east,
+            width=0.6\textwidth,
+            height=0.45\textwidth,
+        ]
+        \addplot [ForestGreen, mark=none, line width=1pt]
+            table [col sep=comma, discard if not={omega}{0.0774263682681127}, x=k, y=err]
+                {res/proximal/2d_avg_error_20433484_1db.csv};
+        \addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
+        \addplot [NavyBlue, mark=none, line width=1pt]
+            table [col sep=comma, discard if not={omega}{0.0774263682681127}, x=k, y=err]
+                {res/proximal/2d_avg_error_20433484_3db.csv};
+        \addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
+        \addplot [RedOrange, mark=none, line width=1pt]
+            table [col sep=comma, discard if not={omega}{0.052233450742668434}, x=k, y=err]
+                {res/proximal/2d_avg_error_20433484_5db.csv};
+        \addlegendentry{$E_b / N_0 = \SI{5}{dB}$}
+        \addplot [RoyalPurple, mark=none, line width=1pt]
+            table [col sep=comma, discard if not={omega}{0.052233450742668434}, x=k, y=err]
+                {res/proximal/2d_avg_error_20433484_8db.csv};
+        \addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
+        \end{axis}
+    \end{tikzpicture}
+
+    \caption{Average error for $\SI{500000}{}$ decodings\protect\footnotemark{}}
+\end{figure}%
+%
+\footnotetext{(3,6) regular \ac{LDPC} code with n = 204, k = 102
+    \cite[\text{204.33.484}]{mackay_enc}; $\gamma=0.05, \omega = 0.05, K=200, \eta=1.5$
+}%
+%
 
 Changing the parameter $\eta$ does not appear to have a significant effect on
 the decoding performance when keeping the value within a reasonable window

latex/thesis/res/proximal/2d_avg_error_20433484_1db_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 397.47346705402015,
+    "name": "2d_avg_error_20433484",
+    "platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
+    "SNR": 1,
+    "K": 200,
+    "end_time": "2023-01-24 23:34:34.589607"
+}

latex/thesis/res/proximal/2d_avg_error_20433484_3db_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 297.83671288599726,
+    "name": "2d_avg_error_20433484",
+    "platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
+    "SNR": 3,
+    "K": 200,
+    "end_time": "2023-01-24 23:26:41.141614"
+}

latex/thesis/res/proximal/2d_avg_error_20433484_5db_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 555.086431461008,
+    "name": "2d_avg_error_20433484",
+    "platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
+    "SNR": 5,
+    "K": 200,
+    "end_time": "2023-01-24 23:17:21.185610"
+}

latex/thesis/res/proximal/2d_avg_error_20433484_8db_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 870.158950668003,
+    "name": "2d_avg_error_20433484",
+    "platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
+    "SNR": 8,
+    "K": 200,
+    "end_time": "2023-01-24 23:06:24.712365"
+}