\chapter{Theoretical Background}%
\label{chapter:theoretical_background}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Preliminaries: Channel Model and Modulation}
\label{sec:theo:Preliminaries: Channel Model and Modulation}

\begin{itemize}
    \item AWGN
    \item BPSK
\end{itemize}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Notation}
\label{sec:theo:Notation}

\begin{itemize}
    \item General remarks on notation (matrices, PDF, etc.)
    \item Diagram from midterm presentation
\end{itemize}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Channel Coding with LDPC Codes}
\label{sec:theo:Channel Coding with LDPC Codes}

\begin{itemize}
    \item Introduction
    \item Binary linear codes
    \item LDPC codes
\end{itemize}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Decoding LDPC Codes using Belief Propagation}
\label{sec:theo:Decoding LDPC Codes using Belief Propagation}

\begin{itemize}
    \item Introduction to message passing
    \item Overview of BP altorithm
\end{itemize}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Optimization Methods}
\label{sec:theo:Optimization Methods}

\begin{itemize}
    \item ADMM
    \item Proximal gradient method
\end{itemize}

