From 052bb57834e5cbaa14f8da4e734591db9fec818f Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Fri, 27 Jan 2023 02:30:41 +0100 Subject: [PATCH] Incorporated proposals from test presentation; Fixed pseudocode listings --- latex/presentations/midterm/presentation.tex | 2 +- .../midterm/sections/decoding_algorithms.tex | 8 ++++--- .../midterm/sections/examination_results.tex | 24 ++++++++++++------- .../sections/forthcoming_examination.tex | 2 +- 4 files changed, 23 insertions(+), 13 deletions(-) diff --git a/latex/presentations/midterm/presentation.tex b/latex/presentations/midterm/presentation.tex index 8160657..93c799d 100644 --- a/latex/presentations/midterm/presentation.tex +++ b/latex/presentations/midterm/presentation.tex @@ -196,7 +196,7 @@ basicstyle=\normalfont, columns=fullflexible, keywordstyle=\color{black}\bfseries, - keywords={a, for, end, do, return, b} % add the keywords you want, or load + keywords={a, for, end, do, return, if, b} % add the keywords you want, or load % a language as Rubens explains in his comment above. numbers=left, xleftmargin=.04\textwidth, diff --git a/latex/presentations/midterm/sections/decoding_algorithms.tex b/latex/presentations/midterm/sections/decoding_algorithms.tex index b21965f..b99d64c 100644 --- a/latex/presentations/midterm/sections/decoding_algorithms.tex +++ b/latex/presentations/midterm/sections/decoding_algorithms.tex @@ -16,7 +16,7 @@ = \argmax_{x\in\mathbb{R}^n} f_{\boldsymbol{Y}}\left( \boldsymbol{y} | \boldsymbol{x} \right) f_{\boldsymbol{X}}\left( \boldsymbol{x} \right) - = \argmax_{x\in\mathbb{R^n}} + = \argmax_{x\in\mathbb{R}^n} e^{-L\left( \boldsymbol{y} | \boldsymbol{x}\right)} f_{\boldsymbol{X}}\left( \boldsymbol{x} \right) \end{align*} @@ -70,7 +70,7 @@ \left( \boldsymbol{y} | \boldsymbol{x} \right) \right) \end{align*} \note{Notational difference between $f$ and $f_X$ or $f_Y$} - \item Code proximal operator \cite{proximal_algorithms}: + \item Proximal operator \cite{proximal_algorithms}: \begin{align*} \text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv \argmin_{\boldsymbol{t}\in\mathbb{R}^n} \left( @@ -108,7 +108,9 @@ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ - If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ + if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do + return $\boldsymbol{\hat{c}}$ + end if end for return $\boldsymbol{\hat{c}}$ \end{algorithm} diff --git a/latex/presentations/midterm/sections/examination_results.tex b/latex/presentations/midterm/sections/examination_results.tex index 08ca7ac..ae56b38 100644 --- a/latex/presentations/midterm/sections/examination_results.tex +++ b/latex/presentations/midterm/sections/examination_results.tex @@ -410,7 +410,9 @@ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ - If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ + if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do + return $\boldsymbol{\hat{c}}$ + end if end for return $\boldsymbol{\hat{c}}$ \end{algorithm} @@ -981,6 +983,8 @@ return $\boldsymbol{\hat{c}}$ \frametitle{Proximal Decoding: Improvement using ``ML-on-List''} \setcounter{footnote}{0} + \vspace*{-0.5cm} + \begin{itemize} \item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating \end{itemize} @@ -991,13 +995,15 @@ return $\boldsymbol{\hat{c}}$ \begin{figure} \centering - \begin{algorithm}[caption={}, label={}] + \begin{algorithm}[caption={}, label={}, basicstyle=\fontsize{9.5}{11.5}\selectfont] $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ - If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ + if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do + return $\boldsymbol{\hat{c}}$ + end if end for return $\boldsymbol{\hat{c}}$ \end{algorithm} @@ -1011,18 +1017,20 @@ return $\boldsymbol{\hat{c}}$ \begin{figure} \centering - \begin{algorithm}[caption={}, label={}] + \begin{algorithm}[caption={}, label={}, basicstyle=\fontsize{9.5}{11.5}\selectfont] $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ - If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ + if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ + return $\boldsymbol{\hat{c}}$ + end if end for $\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$ -$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_n\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$ -$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_n, \boldsymbol{\hat{c}} \right) \forall n \in \left[ 1 : N-1 \right]}$ -$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_n, \boldsymbol{\hat{c}} \right)}$ +$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_i\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$ +$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\tilde{c}}_i}$ +$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_i\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right)}$ \end{algorithm} \caption{Improved proximal decoding algorithm} diff --git a/latex/presentations/midterm/sections/forthcoming_examination.tex b/latex/presentations/midterm/sections/forthcoming_examination.tex index a5e8e15..16db46a 100644 --- a/latex/presentations/midterm/sections/forthcoming_examination.tex +++ b/latex/presentations/midterm/sections/forthcoming_examination.tex @@ -3,7 +3,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Forth Exam LP Decoding}% +\subsection{LP Decoding}% \label{sub:Forth Exam LP Decoding} \begin{frame}[t]