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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,
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
of a hypercube and the goal is to find that point $\boldsymbol{x}$,
\todo{$\boldsymbol{x}$? Or some other variable?}
@ -255,7 +255,8 @@ immediately approximalted by a gradient-descent step:%
\hspace{5mm} \gamma \text{ small}
.\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*}
\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}%
\label{chapter:theoretical_background}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Preliminaries: Channel Model and Modulation}
\label{sec:theo:Preliminaries: Channel Model and Modulation}
\begin{itemize}
\item \Ac{AWGN}
\item \Ac{BPSK}
\end{itemize}
In this chapter, the theoretical background necessary to understand this
work is given.
First, the used notation is clarified.
The physical aspects are detailed - the used modulation scheme and channel model.
A short introduction of channel coding with binary linear codes and especially
\ac{LDPC} codes is given.
The established methods of decoding LPDC codes are briefly explained.
Lastly, the optimization methods utilized are described.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -21,8 +20,8 @@
%
\begin{itemize}
\item General remarks on notation (matrices, PDF, etc.)
\item \sout{Diagram from midterm presentation}
\item General remarks on notation (matrices, \ldots)
\item Probabilistic quantities (random variables, \acp{PDF}, \ldots)
\end{itemize}
%
@ -59,6 +58,17 @@
\caption{Overview of notation}
\label{fig:notation}
\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}
\item Introduction
\item Binary linear codes
\item \Ac{LDPC} codes
\item \Ac{LDPC} codes (especially $i$, $j$, parity check matrix $\boldsymbol{H}$, etc.)
\end{itemize}