diff --git a/latex/presentations/midterm/presentation.bib b/latex/presentations/midterm/presentation.bib index 32afbe2..b96b971 100644 --- a/latex/presentations/midterm/presentation.bib +++ b/latex/presentations/midterm/presentation.bib @@ -77,9 +77,9 @@ institution = {KIT}, } -@BOOK{distr_opt_book, +@book{distr_opt_book, author = {Boyd, Stephen and Parikh, Neal and Chu, Eric and Peleato, Borja and Eckstein, Jonathan}, - booktitle = {Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers}, + title = {Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers}, year = {2011}, volume = {}, number = {}, diff --git a/latex/presentations/midterm/sections/examination_results.tex b/latex/presentations/midterm/sections/examination_results.tex index 2a60aeb..078e107 100644 --- a/latex/presentations/midterm/sections/examination_results.tex +++ b/latex/presentations/midterm/sections/examination_results.tex @@ -1504,74 +1504,23 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d \end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\begin{frame}[t, fragile] -% \frametitle{Proximal Decoding: Improvement using ``ML-on-List''} -% \setcounter{footnote}{0} -% -% \begin{itemize} -% \item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating -% \end{itemize} -% -% \begin{minipage}[t]{.48\textwidth} -% \centering -% -% \begin{figure} -% \centering -% -% \begin{algorithm}[caption={}, label={}, -% basicstyle=\fontsize{7.5}{9.5}\selectfont -% ] -%$\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} -% -% \caption{Proximal decoding algorithm \cite{proximal_paper}} -% \end{figure} -% -% \end{minipage}% -% \hfill\begin{minipage}[t]{.48\textwidth} -% \centering -% \begin{figure} -% \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) $ -% $\textcolor{KITblue}{\text{If }\boldsymbol{\hat{x}}\text{ passes the parity check condition, output }\boldsymbol{\hat{x}}}$ -%end for -%$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$ -%$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{x}}_n\text{ of }\boldsymbol{\hat{x}}\text{ with the }N\text{ bits modified.}}$ -%$\textcolor{KITblue}{\text{Compute }\langle \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \rangle \forall n \in \left[ 1 : N-1 \right]}$ -%$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{x}}_n\text{ with lowest }\langle \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \rangle}$ -% \end{algorithm} -% -% \caption{Hybrid proximal \& ML decoding algorithm} -% \end{figure} -% \end{minipage} -%\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{ADMM: Examination Results}% -%\label{sub:Ex ADMM} -% -%\begin{frame}[t] -% \frametitle{ADMM} -% -% \todo{TODO} -%\end{frame} - +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}[t] + \frametitle{Conclusion} + + \begin{itemize} + \item Analysis of proximal decoding for AWGN channels: + \begin{itemize} + \item Error coding performance (BER, FER, decoding failures) + \item Computational performance ($\mathcal{O}\left( n \right) $ time complexity, + fast implementation possible) + \item Number of iterations required independant of SNR + \item Operation during iteration (oscillation of estimate) + \end{itemize} + \item Suggestion for improvement of proximal decoding: + \begin{itemize} + \item Addidion of ``ML-on-list'' step + \item $\sim\SI{1}{dB}$ gain under certain conditions + \end{itemize} + \end{itemize} +\end{frame} diff --git a/latex/presentations/midterm/sections/forthcoming_examination.tex b/latex/presentations/midterm/sections/forthcoming_examination.tex index b372a8e..d2d1ab8 100644 --- a/latex/presentations/midterm/sections/forthcoming_examination.tex +++ b/latex/presentations/midterm/sections/forthcoming_examination.tex @@ -16,7 +16,7 @@ \item ADMM is intended to blend the decomposability of dual ascent with the superior convergence properties of the method of multipliers \cite{distr_opt_book} - \item Recently, ADMM has been proposed for efficient LP Decoding + \item ADMM has been proposed for efficient LP Decoding \cite{efficient_lp_dec_admm} \end{itemize} \item Compare ADMM implementation with Proximal Decoding implementation with respect to