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Added footnotes mentioning used code; Added Hybrid algorithm

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Andreas Tsouchlos 2023-01-23 20:07:40 +01:00
parent ce2c22d7db
commit 6939c6bcc5
3 changed files with 284 additions and 137 deletions
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2
latex/presentations/midterm/sections/decoding_algorithms.tex
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@ -58,7 +58,7 @@
\left( \boldsymbol{y} | \boldsymbol{x} \right) \right) \left( \boldsymbol{y} | \boldsymbol{x} \right) \right)
\end{align*} \end{align*}
\note{Notational difference between $f$ and $f_X$ or $f_Y$} \note{Notational difference between $f$ and $f_X$ or $f_Y$}
\item Code proximal operator: \item Code proximal operator \cite{proximal_algorithms}:
\begin{align*} \begin{align*}
\text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv \text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv
arg\min_{\boldsymbol{z}\in\mathbb{R}} \left( arg\min_{\boldsymbol{z}\in\mathbb{R}} \left(

401
latex/presentations/midterm/sections/examination_results.tex
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@ -3,14 +3,17 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Proximal Decoder}% \subsection{Proximal Decoding}%
\label{sub:Ex Proximal Decoder} \label{sub:Ex Proximal Decoding}
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoder: Examination Results} \frametitle{Proximal Decoding: Bit Error Rate and Performance}
\begin{itemize} \begin{itemize}
\item AWGN Channel - (3,6) regular LDPC Code with $n=204, k=102$: \item Comparison of simulation
\vspace{2mm} \footnote{(3,6) regular LDPC Code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
with results of Wadayama and Takabe
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -62,67 +65,86 @@
\item $\mathcal{O}\left(n \right) $ time complexity - same as BP; \item $\mathcal{O}\left(n \right) $ time complexity - same as BP;
Only multiplication and addition necessary \cite{proximal_paper} Only multiplication and addition necessary \cite{proximal_paper}
\item Measured Performance: Between $\SI{0.5}{\mega\bit / \second}$ and \item Measured Performance: Between $\SI{0.5}{\mega\bit / \second}$ and
$\SI{2.5}{\mega\bit / \second}$ - Intel Core i7-7700HQ @ 2.80GHz\\ $\SI{2.5}{\mega\bit / \second}$ - Intel Core i7-7700HQ @ 2.80GHz%
($\sim \SI{10}{\second}$ for the shown plot) % \\ ($\sim \SI{10}{\second}$ for the shown plot)
\todo{Use the shown bitrate, or half?
($n_{iterations} \cdot n$ or $n_{iterations} \cdot k$?)}
\end{itemize} \end{itemize}
\vspace{3mm}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoder: Choice of $\gamma$} \frametitle{Proximal Decoding: Choice of $\gamma$}
\setcounter{footnote}{0}
\begin{figure}[H] \begin{itemize}
\item Comparison of simulation
\footnote{(3,6) regular LDPC Code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
results for different values of $\gamma$
\end{itemize}
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.5\textwidth}
\centering
\begin{tikzpicture}[scale=0.52]
\begin{semilogyaxis}[xlabel={SNR}, ylabel={BER},
grid=both, grid style={line width=.1pt},
legend style={at={(0.05,0.05)},anchor=south west},
ymin=3e-7, ymax=1.5,]
\foreach \gamma in {0.01, 0.05, 0.15}{
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{\gamma}] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\legend{\gamma}
}
\legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
\end{semilogyaxis}
\end{tikzpicture}
\end{subfigure}%
\begin{subfigure}[c]{0.5\textwidth}
\centering \centering
\begin{subfigure}[c]{0.5\textwidth} \begin{tikzpicture}[scale=0.55]
\centering \begin{axis}[view={75}{60},
zmode=log,
xlabel={SNR},
ylabel={$\gamma$},
zlabel={BER},]
\addplot3[surf, mesh/rows=17, mesh/cols=14, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
\addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.05$}
\addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.01$}
\addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.15$}
\end{axis}
\end{tikzpicture}
\end{subfigure}
\begin{tikzpicture}[scale=0.52] \caption{BER for $\omega = 0.05, K=100$}
\begin{semilogyaxis}[xlabel={SNR}, ylabel={BER}, \label{fig:ber_3d}
grid=both, grid style={line width=.1pt}, \end{figure}
legend style={at={(0.05,0.05)},anchor=south west},
ymin=3e-7, ymax=1.5,]
\foreach \gamma in {0.01, 0.05, 0.15}{
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{\gamma}] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\legend{\gamma}
}
\legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
\end{semilogyaxis}
\end{tikzpicture}
\end{subfigure}%
\begin{subfigure}[c]{0.5\textwidth}
\centering
\begin{tikzpicture}[scale=0.7] \begin{itemize}
\begin{axis}[view={75}{60}, \item Not great benefit in finding the optimal value for $\gamma$
zmode=log, \end{itemize}
xlabel={SNR}, \vspace{3mm}
ylabel={$\gamma$},
zlabel={BER},]
\addplot3[surf, mesh/rows=17, mesh/cols=14, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
\addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.05$}
\addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.01$}
\addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.15$}
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{BER for $\omega = 0.05, K=100$}
\label{fig:ber_3d}
\end{figure}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t, fragile] \begin{frame}[t, fragile]
\frametitle{Proximal Decoder: Frame Error Rate} \frametitle{Proximal Decoding: Frame Error Rate}
\setcounter{footnote}{0}
\begin{itemize}
\item Comparison of simulated
\footnote{(3,6) regular LDPC Code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
BER and FER
\end{itemize}
\begin{minipage}{.4\textwidth} \begin{minipage}{.4\textwidth}
\centering \centering
@ -143,11 +165,11 @@ Output $\boldsymbol{\hat{x}}$
\end{minipage}% \end{minipage}%
\begin{minipage}{.6\textwidth} \begin{minipage}{.6\textwidth}
\centering \centering
\begin{figure}[H] \begin{figure}[H]
\vspace*{-8mm}
\centering \centering
\begin{tikzpicture}[scale=0.45] \begin{tikzpicture}[scale=0.42]
\begin{axis}[ \begin{axis}[
grid=both, grid=both,
xlabel={SNR}, ylabel={BER}, xlabel={SNR}, ylabel={BER},
@ -165,8 +187,8 @@ Output $\boldsymbol{\hat{x}}$
{res/2d_ber_fer_dfr_20433484_proximal.csv}; {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.05$} \addlegendentry{$\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture}\\ \end{tikzpicture}
\begin{tikzpicture}[scale=0.45] \begin{tikzpicture}[scale=0.42]
\begin{axis}[ \begin{axis}[
grid=both, grid=both,
xlabel={SNR}, ylabel={FER}, xlabel={SNR}, ylabel={FER},
@ -184,8 +206,8 @@ Output $\boldsymbol{\hat{x}}$
{res/2d_ber_fer_dfr_20433484_proximal.csv}; {res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{$\gamma = 0.05$} \addlegendentry{$\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}\\
\begin{tikzpicture}[scale=0.45] \begin{tikzpicture}[scale=0.42]
\begin{axis}[ \begin{axis}[
grid=both, grid=both,
xlabel={SNR}, ylabel={Decoding Failure Rate}, xlabel={SNR}, ylabel={Decoding Failure Rate},
@ -212,84 +234,209 @@ Output $\boldsymbol{\hat{x}}$
\end{frame} \end{frame}
\begin{frame}[t] \newcommand{\tikzmarknew}[1]{\tikz[overlay,remember picture] \node (#1) {};}
\frametitle{title}
\begin{figure}[H] \newcommand*{\AddNote}[4]{%
\begin{tikzpicture}[overlay, remember picture]
\draw [decoration={brace,amplitude=0.5em},decorate,ultra thick]
($(#3)!([yshift=1.5ex]#1)!($(#3)-(0,1)$)$) --
($(#3)!(#2)!($(#3)-(0,1)$)$)
node [align=center, text width=2cm, pos=0.5, anchor=west] {#4};
\end{tikzpicture}
}%
\begin{frame}[t, fragile]
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
\setcounter{footnote}{0}
\begin{itemize}
\item Comparison of proximal \& hybrid-proximal-ML\\
decoding simulation
\footnote{(3,6) regular LDPC Code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
results
\end{itemize}
\begin{minipage}{.4\textwidth}
\centering \centering
\begin{tikzpicture}[scale=0.45] \begin{algorithm}[caption={}, label={},
\begin{axis}[ basicstyle=\fontsize{6.5}{7.5}\selectfont
grid=both,
xlabel={SNR}, ylabel={BER},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
] ]
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}] $\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$$\hspace{4.185cm}\tikzmarknew{prox-start}$
% {res/2d_ber_fer_dfr_20433484.csv}; for $k=0$ to $K-1$ do
% \addlegendentry{$\gamma = 0.15$} $\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}] Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
% {res/2d_ber_fer_dfr_20433484.csv}; $\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
% \addlegendentry{$\gamma = 0.01$} $\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] If $\boldsymbol{\hat{x}}$ passes the parity check condition, output $\boldsymbol{\hat{x}}$
{res/2d_ber_fer_dfr_20433484_proximal.csv}; end for $\tikzmarknew{prox-end}$
\addlegendentry{proximal} Find $N$ most probably wrong bits $\hspace{2cm}\tikzmarknew{ml-start}$
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] Generate variations $\boldsymbol{\tilde{x}}_n$ of $\boldsymbol{\hat{x}}$ with the $N$ bits modified
{res/2d_ber_fer_dfr_20433484_hybrid.csv}; Compute $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right) \forall n \in \left[ 1 : N-1 \right] $
\addlegendentry{hybrid prox. \& ML} Output $\boldsymbol{\tilde{x}}_n$ with lowest $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right)$ $\tikzmarknew{ml-end}$
\end{axis} \end{algorithm}
\end{tikzpicture}\\
\begin{tikzpicture}[scale=0.45]
\begin{axis}[
grid=both,
xlabel={SNR}, ylabel={FER},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
]
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.15$}
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.01$}
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{proximal}
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
\addlegendentry{hybrid prox. \& ML}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[scale=0.45]
\begin{axis}[
grid=both,
xlabel={SNR}, ylabel={Decoding Failure Rate},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
]
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.15$}
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.01$}
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{proximal}
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
\addlegendentry{hybrid prox. \& ML}
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200$} \AddNote{prox-start}{prox-end}{prox-start}{\small Proximal\\Decoding}
\label{fig:simulation_results_hybrid} \AddNote{ml-start}{ml-end}{ml-start}{\small ML-on-List}
\end{figure} \end{minipage}%
\begin{minipage}{.6\textwidth}
\centering
\begin{figure}[H]
\centering
\vspace*{-12mm}
\begin{tikzpicture}[scale=0.42]
\begin{axis}[
grid=both,
xlabel={SNR}, ylabel={BER},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
]
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.15$}
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.01$}
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{proximal}
\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
\addlegendentry{hybrid prox. \& ML}
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[scale=0.42]
\begin{axis}[
grid=both,
xlabel={SNR}, ylabel={FER},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
]
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.15$}
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.01$}
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{proximal}
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
\addlegendentry{hybrid prox. \& ML}
\end{axis}
\end{tikzpicture}\\
\begin{tikzpicture}[scale=0.42]
\begin{axis}[
grid=both,
xlabel={SNR}, ylabel={Decoding Failure Rate},
ymode=log,
legend style={at={(0.05,0.05)},anchor=south west},
ymax=1.5, ymin=3e-8,
]
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.15$}
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
% {res/2d_ber_fer_dfr_20433484.csv};
% \addlegendentry{$\gamma = 0.01$}
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_proximal.csv};
\addlegendentry{proximal}
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
\addlegendentry{hybrid prox. \& ML}
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
\label{fig:simulation_results_hybrid}
\end{figure}
\end{minipage}
\end{frame} \end{frame}
%\begin{frame}[t]
% \frametitle{Proximal Decoding: Improvement}
% \begin{figure}[H]
% \centering
%
% \begin{tikzpicture}[scale=0.45]
% \begin{axis}[
% grid=both,
% xlabel={SNR}, ylabel={BER},
% ymode=log,
% legend style={at={(0.05,0.05)},anchor=south west},
% ymax=1.5, ymin=3e-8,
% ]
%% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.15$}
%% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.01$}
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
% \addlegendentry{proximal}
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
% \addlegendentry{hybrid prox. \& ML}
% \end{axis}
% \end{tikzpicture}
% \begin{tikzpicture}[scale=0.45]
% \begin{axis}[
% grid=both,
% xlabel={SNR}, ylabel={FER},
% ymode=log,
% legend style={at={(0.05,0.05)},anchor=south west},
% ymax=1.5, ymin=3e-8,
% ]
%% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.15$}
%% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.01$}
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
% \addlegendentry{proximal}
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
% \addlegendentry{hybrid prox. \& ML}
% \end{axis}
% \end{tikzpicture}\\
% \begin{tikzpicture}[scale=0.45]
% \begin{axis}[
% grid=both,
% xlabel={SNR}, ylabel={Decoding Failure Rate},
% ymode=log,
% legend style={at={(0.05,0.05)},anchor=south west},
% ymax=1.5, ymin=3e-8,
% ]
%% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.15$}
%% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
%% {res/2d_ber_fer_dfr_20433484.csv};
%% \addlegendentry{$\gamma = 0.01$}
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
% \addlegendentry{proximal}
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
% \addlegendentry{hybrid prox. \& ML}
% \end{axis}
% \end{tikzpicture}
%
% \caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, \SI{12}{\bit}$}
% \label{fig:simulation_results_hybrid}
% \end{figure}
%
%\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{ADMM: Examination Results}% \subsection{ADMM: Examination Results}%

4
latex/presentations/midterm/sections/theoretical_background.tex
View File

@ -11,11 +11,11 @@
\begin{itemize} \begin{itemize}
\item The general [ML] decoding problem for linear codes and the general problem \item The general [ML] decoding problem for linear codes and the general problem
of finding the weights of a linear code are both NP-complete. \cite{ml_np_hard_proof} of finding the weights of a linear code are both NP-complete. \cite{ml_np_hard_proof}
\item The standard message-passing algorithms used for decoding [LDPC and turbo codes]
are often difficult to analyze. \cite{feldman_thesis}
\item The iterative message–passing algorithms preffered in practice do not guarantee \item The iterative message–passing algorithms preffered in practice do not guarantee
optimality and may fail to decode correctly when the graph contains cycles optimality and may fail to decode correctly when the graph contains cycles
\cite{ldpc_conv} \cite{ldpc_conv}
\item The standard message-passing algorithms used for decoding [LDPC and turbo codes]
are often difficult to analyze. \cite{feldman_thesis}
\end{itemize} \end{itemize}
\end{frame} \end{frame}