diff --git a/latex/thesis/chapters/proximal_decoding.tex b/latex/thesis/chapters/proximal_decoding.tex index c14662e..6540fcd 100644 --- a/latex/thesis/chapters/proximal_decoding.tex +++ b/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 diff --git 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