diff --git a/latex/presentations/midterm/presentation.tex b/latex/presentations/midterm/presentation.tex index b22539f..d92b9fa 100644 --- a/latex/presentations/midterm/presentation.tex +++ b/latex/presentations/midterm/presentation.tex @@ -13,6 +13,12 @@ \usepackage{listings} \usepackage{graphicx} \usepackage{xcolor} +%\geometry{textheight=17.07cm,textwidth=6.9cm} +%\usepackage{pgfpages} +%\pgfpagesuselayout{resize to}[physical paper height=17.07cm, +% physical paper width=6.9cm] +%\setbeamertemplate{note page}[plain] +%\setbeameroption{show notes on second screen=right} \usepgfplotslibrary{colorbrewer} \setlength {\marginparwidth }{2cm} diff --git a/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484.csv b/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484.csv new file mode 100644 index 0000000..47a9a39 --- /dev/null +++ b/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484.csv @@ -0,0 +1,171 @@ +SNR,gamma,BER,FER,DFR,num_iterations 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+3.5,0.15,0.2707861990950226,0.9711538461538461,0.4926829268292683,104.0 +4.0,0.01,0.008812513769552765,0.5674157303370787,0.36200716845878134,178.0 +4.0,0.05,0.0019857029388403494,0.08022239872915012,0.07426470588235294,1259.0 +4.0,0.15,0.27478468022723107,0.9439252336448598,0.4855769230769231,107.0 +4.5,0.01,0.004626022594468251,0.3344370860927152,0.2506203473945409,302.0 +4.5,0.05,0.0006845708267509215,0.031911532385466033,0.030924678505817513,3165.0 +4.5,0.15,0.2821402145763966,0.9528301886792453,0.48792270531400966,106.0 +5.0,0.01,0.0017591120532297003,0.15165165165165165,0.1316818774445893,666.0 +5.0,0.05,0.00021886964617101427,0.010585892464102296,0.010475005185646131,9541.0 +5.0,0.15,0.2730257240510883,0.926605504587156,0.48095238095238096,109.0 +5.5,0.01,0.0006439016284479894,0.061138014527845036,0.057615516257843696,1652.0 +5.5,0.05,6.1029411764705884e-05,0.00305,0.0030407257863516277,20000.0 +5.5,0.15,0.24632352941176472,0.8145161290322581,0.4488888888888889,124.0 diff --git a/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484_metadata.json b/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484_metadata.json new file mode 100644 index 0000000..0104eb0 --- /dev/null +++ b/latex/presentations/midterm/res/2d_ber_fer_dfr_20433484_metadata.json @@ -0,0 +1,8 @@ +{ + "duration": 38.217501369000274, + "name": "2d_BER_FER_DFR_20433484", + "platform": "Linux-6.1.3-arch1-1-x86_64-with-glibc2.36", + "omega": 0.05, + "K": 100, + "end_time": "2023-01-07 09:31:11.720513" +} \ No newline at end of file diff --git a/latex/presentations/midterm/res/ber_paper.pdf b/latex/presentations/midterm/res/ber_paper.pdf new file mode 100644 index 0000000..fdd5e6c Binary files /dev/null and b/latex/presentations/midterm/res/ber_paper.pdf differ diff --git a/latex/presentations/midterm/sections/decoding_algorithms.tex b/latex/presentations/midterm/sections/decoding_algorithms.tex index a355237..bc79340 100644 --- a/latex/presentations/midterm/sections/decoding_algorithms.tex +++ b/latex/presentations/midterm/sections/decoding_algorithms.tex @@ -16,7 +16,12 @@ \underbrace{\sum_{j=1}^{n} \left( x_j^2 - 1 \right)^2}_{\text{Bipolar constraint}} + \underbrace{\sum_{i=1}^{m} \left[ \left( \prod_{j\in\mathcal{A}\left( i \right)} x_j\right) -1 \right]^2} - _{\text{Parity constraint}} + _{\text{Parity constraint}}, + \hspace{5mm}\mathcal{A}\left( i \right) \equiv \left\{ + j | j\in \mathcal{J}, + \boldsymbol{H}_{i,j} = 1 + \right\}, + i \in \mathcal{I} \end{align*} \item Approximation of prior PDF: \begin{align*} @@ -54,7 +59,7 @@ = - \ln\left( f_{\boldsymbol{Y}} \left( \boldsymbol{y} | \boldsymbol{x} \right) \right) \end{align*} - \todo{Note about explaning 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: \begin{align*} \text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv diff --git a/latex/presentations/midterm/sections/examination_results.tex b/latex/presentations/midterm/sections/examination_results.tex index aca41ab..6c91547 100644 --- a/latex/presentations/midterm/sections/examination_results.tex +++ b/latex/presentations/midterm/sections/examination_results.tex @@ -7,14 +7,283 @@ \label{sub:Ex Proximal Decoder} \begin{frame}[t] - \frametitle{Proximal Decoder} + \frametitle{Proximal Decoder: Examination Results} + \begin{itemize} + \item AWGN Channel - LDPC Code with $n=204, k=102$: + \vspace{2mm} + \begin{figure}[H] + \centering - \todo{TODO} + \begin{subfigure}{0.5\textwidth} + \centering + + \begin{tikzpicture}[scale=0.45] + \begin{axis}[ + grid=both, + xlabel={SNR (dB)}, ylabel={Bit Error Rate}, + ymode=log, + legend style={at={(0.05,0.05)},anchor=south west}, + width=11.5cm, + height=8cm, + ytick={0, 10e-1, 10e-2, 10e-3, 10e-4}, + xtick={1, 2, 3, 4, 5}, + ymax=1.2, ymin=0.8e-4, + ] + \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \end{axis} + \end{tikzpicture} + + \caption{Simulation results for $\omega = 0.05, K=100$} + \label{fig:sim_results_prox} + \end{subfigure}% + \begin{subfigure}{0.5\textwidth} + \centering + + \includegraphics[scale=0.6]{res/ber_paper} + + \caption{Results from ``Proximal Decoding for LDPC Codes''} + \label{fig:sim_results_prox} + \end{subfigure}% + + \end{figure} + + \item Performance: $2800 \text{ transm.} / s$ - Intel Core i7-7700HQ @ 2.80GHz\\ + ($\sim 10s$ for the shown plot) + \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{ADMM}% +\begin{frame}[t] + \frametitle{Proximal Decoder: Choice of $\gamma$} + + \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}] + \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.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{axis}[view={75}{60}, + zmode=log, + xlabel={SNR}, + ylabel={$\gamma$}, + zlabel={BER}] + \addplot3[surf, mesh/rows=17, mesh/cols=10, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv}; + \addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $} + \addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv}; + \addlegendentry{$\gamma = 0.05$} + \addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv}; + \addlegendentry{$\gamma = 0.01$} + \addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv}; + \addlegendentry{$\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} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[t, fragile] + \frametitle{Proximal Decoder: Frame Error Rate} + + \begin{minipage}{.4\textwidth} + \centering + + \begin{algorithm}[caption={}, label={}, + basicstyle=\fontsize{7.5}{9.5}\selectfont + ] +$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$ +for $k=0$ to $K-1$ do + $\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $ + Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$ + $\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $ + $\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $ + If $\boldsymbol{\hat{x}}$ passes the parity check condition, break the loop. +end for +Output $\boldsymbol{\hat{x}}$ + \end{algorithm} + \end{minipage}% + \begin{minipage}{.6\textwidth} + \centering + + \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=0.8e-4, + ] + \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \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=0.8e-4, + ] + \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \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=0.8e-4, + ] + \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \end{axis} + \end{tikzpicture} + + \caption{Simulation results for $\omega = 0.05, K=100$} + \label{fig:simulation_results} + \end{figure} + \end{minipage} +\end{frame} + + +\begin{frame}[t] + \frametitle{title} + \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=0.8e-5, + ] +% \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \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 $\gamma = 0.05$} + \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=0.8e-5, + ] +% \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \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 $\gamma = 0.05$} + \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=0.8e-5, + ] +% \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.csv}; + \addlegendentry{$\gamma = 0.05$} + \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 $\gamma = 0.05$} + \end{axis} + \end{tikzpicture} + + \caption{Simulation results for $\omega = 0.05, K=100$} + \label{fig:simulation_results} + \end{figure} + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{ADMM: Examination Results}% \label{sub:Ex ADMM} \begin{frame}[t] diff --git a/latex/presentations/midterm/sections/theoretical_background.tex b/latex/presentations/midterm/sections/theoretical_background.tex index 1353a55..cbbbf17 100644 --- a/latex/presentations/midterm/sections/theoretical_background.tex +++ b/latex/presentations/midterm/sections/theoretical_background.tex @@ -56,7 +56,6 @@ \left(0,\frac{1}{2}\left(\frac{k}{n}\frac{E_b}{N_0}\right)^{-1}\right), \hspace{2mm} \boldsymbol{y}, \boldsymbol{n} \in \mathbb{R}^n \end{align*} - \todo{Why $\frac{1}{2}$} \item All zeros assumption: \begin{align*} \boldsymbol{c} = 0 @@ -171,6 +170,7 @@ \right\}, j \in \mathcal{J} \end{align*} + \todo{Is this correct? Shouldn't i and j be switched around?} \item ``Illegal configurations'' \begin{align*} S \subseteq N\left( j \right), \left| S \right| \text{odd} @@ -237,7 +237,8 @@ \caption{Relaxed polytope for $n=3$} \end{figure} \end{minipage} - \todo{How is this a relaxation and not just an alternative formulation?} + \todo{How is this a relaxation and not just an alternative formulation? + We have just switched out valid codewords for invalid ones} \todo{Is LP Relaxation relevant as theoretical background?} \end{frame}