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Added introduction to theoretical background; minor changes to decoding techniques

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Andreas Tsouchlos 2023-02-15 18:08:11 +01:00
parent 4584989ae5
commit 773f3b1109
2 changed files with 25 additions and 14 deletions
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5
latex/thesis/chapters/decoding_techniques.tex
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@ -40,7 +40,7 @@ $f$ has to be minimized under certain constraints:%
In contrast to the established message-passing decoding algorithms, In contrast to the established message-passing decoding algorithms,
the viewpoint then changes from observing the decoding process in its the viewpoint then changes from observing the decoding process in its
tanner graph based representation (as shown in figure \ref{fig:dec:tanner}) tanner graph representation (as shown in figure \ref{fig:dec:tanner})
into a spacial representation, where the codewords are some of the edges into a spacial representation, where the codewords are some of the edges
of a hypercube and the goal is to find that point $\boldsymbol{x}$, of a hypercube and the goal is to find that point $\boldsymbol{x}$,
\todo{$\boldsymbol{x}$? Or some other variable?} \todo{$\boldsymbol{x}$? Or some other variable?}
@ -255,7 +255,8 @@ immediately approximalted by a gradient-descent step:%
\hspace{5mm} \gamma \text{ small} \hspace{5mm} \gamma \text{ small}
.\end{align*}% .\end{align*}%
% %
The second step thus becomes% The second step thus becomes \todo{Write the formulation optimization problem properly
(as shown in the introductory section)}%
% %
\begin{align*} \begin{align*}
\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right), \boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right),

34
latex/thesis/chapters/theoretical_background.tex
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@ -1,15 +1,14 @@
\chapter{Theoretical Background}% \chapter{Theoretical Background}%
\label{chapter:theoretical_background} \label{chapter:theoretical_background}
In this chapter, the theoretical background necessary to understand this
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% work is given.
\section{Preliminaries: Channel Model and Modulation} First, the used notation is clarified.
\label{sec:theo:Preliminaries: Channel Model and Modulation} The physical aspects are detailed - the used modulation scheme and channel model.
A short introduction of channel coding with binary linear codes and especially
\begin{itemize} \ac{LDPC} codes is given.
\item \Ac{AWGN} The established methods of decoding LPDC codes are briefly explained.
\item \Ac{BPSK} Lastly, the optimization methods utilized are described.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -21,8 +20,8 @@
% %
\begin{itemize} \begin{itemize}
\item General remarks on notation (matrices, PDF, etc.) \item General remarks on notation (matrices, \ldots)
\item \sout{Diagram from midterm presentation} \item Probabilistic quantities (random variables, \acp{PDF}, \ldots)
\end{itemize} \end{itemize}
% %
@ -59,6 +58,17 @@
\caption{Overview of notation} \caption{Overview of notation}
\label{fig:notation} \label{fig:notation}
\end{figure} \end{figure}
\todo{Move figure to 'Channel and Modulation'}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Preliminaries: Channel Model and Modulation}
\label{sec:theo:Preliminaries: Channel Model and Modulation}
\begin{itemize}
\item \Ac{AWGN}
\item \Ac{BPSK}
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -68,7 +78,7 @@
\begin{itemize} \begin{itemize}
\item Introduction \item Introduction
\item Binary linear codes \item Binary linear codes
\item \Ac{LDPC} codes \item \Ac{LDPC} codes (especially $i$, $j$, parity check matrix $\boldsymbol{H}$, etc.)
\end{itemize} \end{itemize}