\chapter{Introduction}% \label{chapter:introduction} \begin{itemize} \item Problem definition \item Motivation \begin{itemize} \item Error floor when decoding with BP (seems to not be persent with LP decoding \cite[Sec. I]{original_admm}) \item Strong theoretical guarantees that allow for better and better approximations of ML decoding \cite[Sec. I]{original_admm} \end{itemize} \item Results summary \end{itemize}