Fixed captions
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@ -109,7 +109,7 @@ return $\tilde{\boldsymbol{c}}$
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\end{subfigure}%
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\end{subfigure}%
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\caption{Comparison of the proximal gradient method and \ac{ADMM}}
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\caption{Comparison of proximal decoding and \ac{LP} decoding using \ac{ADMM}}
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\label{fig:ana:theo_comp_alg}
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\label{fig:ana:theo_comp_alg}
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\end{figure}%
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\end{figure}%
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@ -216,7 +216,7 @@ return $\tilde{\boldsymbol{c}}$
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\end{subfigure}%
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\end{subfigure}%
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\caption{The proximal gradient method and \ac{LP} decoding using \ac{ADMM}
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\caption{Proximal decoding and \ac{LP} decoding using \ac{ADMM}
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as message passing algorithms}
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as message passing algorithms}
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\label{fig:comp:message_passing}
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\label{fig:comp:message_passing}
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\end{figure}%
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\end{figure}%
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@ -297,7 +297,7 @@ Nevertheless, the run time of both the proximal decoding and the \ac{LP}
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decoding using \ac{ADMM} implementations is similar, and both are
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decoding using \ac{ADMM} implementations is similar, and both are
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reasonably performant, owing to the parallelizable structure of the
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reasonably performant, owing to the parallelizable structure of the
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algorithms.
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algorithms.
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%
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\begin{figure}[h]
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\begin{figure}[h]
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\centering
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\centering
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@ -582,7 +582,7 @@ algorithms.
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\end{tikzpicture}
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\end{tikzpicture}
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\end{subfigure}
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\end{subfigure}
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\caption{Comparison of decoding performance of the different decoder
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\caption{Comparison of the decoding performance of the different decoder
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implementations for various codes}
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implementations for various codes}
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\label{fig:comp:prox_admm_dec}
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\label{fig:comp:prox_admm_dec}
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\end{figure}
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\end{figure}
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@ -812,7 +812,7 @@ the $\tilde{\boldsymbol{c}}$ update can then be rewritten as%
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%
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%
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This modified version of the decoding process is depicted in algorithm \ref{alg:admm:mod}.
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This modified version of the decoding process is depicted in algorithm \ref{alg:admm:mod}.
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\begin{genericAlgorithm}[caption={\ac{LP} decoding using \ac{ADMM} algorithm with rewritten
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\begin{genericAlgorithm}[caption={The \ac{LP} decoding using \ac{ADMM} algorithm with rewritten
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update steps}, label={alg:admm:mod},
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update steps}, label={alg:admm:mod},
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basicstyle=\fontsize{11}{16}\selectfont
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basicstyle=\fontsize{11}{16}\selectfont
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]
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]
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@ -1172,7 +1172,7 @@ of one another.
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\caption{Comparison of datapoints from Barman et al. with own simulation results.
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\caption{Comparison of datapoints from Barman et al. with own simulation results.
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``Margulis'' \ac{LDPC} code with $n = 2640$, $k = 1320$
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``Margulis'' \ac{LDPC} code with $n = 2640$, $k = 1320$
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\cite[\text{Margulis2640.1320.3}]{mackay_enc}\protect\footnotemark{}}
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\cite[\text{Margulis2640.1320.3}]{mackay_enc}}
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\label{fig:admm:results}
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\label{fig:admm:results}
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\end{figure}%
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\end{figure}%
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%
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%
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@ -1239,6 +1239,11 @@ with linear behavior.
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Nonetheless, the simulation results roughly match the expected behavior
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Nonetheless, the simulation results roughly match the expected behavior
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following from the theoretical considerations.
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following from the theoretical considerations.
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\begin{figure}[H]
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\centering
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\vspace*{5cm}
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\end{figure}
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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@ -1433,11 +1438,15 @@ following from the theoretical considerations.
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\end{subfigure}
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\end{subfigure}
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\caption{Dependence of average number of iterations required on the parameters
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\caption{Dependence of the average number of iterations required on the parameters
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$\mu$ and $\rho$ for various codes}
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$\mu$ and $\rho$ for $E_b / N_0 = \SI{4}{dB}$ for various codes}
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\label{fig:admm:mu_rho_multiple}
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\label{fig:admm:mu_rho_multiple}
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\end{figure}
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\end{figure}
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\vfill
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\newpage
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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@ -1510,6 +1510,8 @@ the code as well as the chosen parameters.
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\caption{Comparison of the timing requirements of the implementations of proximal
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\caption{Comparison of the timing requirements of the implementations of proximal
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decoding and the improved algorithm}
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decoding and the improved algorithm}
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\label{fig:prox:time_complexity_comp}
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\label{fig:prox:time_complexity_comp}
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\vspace*{10cm}
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\end{figure}
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\end{figure}
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@ -2276,8 +2278,8 @@ the code as well as the chosen parameters.
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\end{tikzpicture}
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\end{tikzpicture}
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\end{subfigure}
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\end{subfigure}
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\caption{Comparison of improvement in decoding performance for various
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\caption{Comparison of the decoding performance of proximal decoding
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codes}
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and the improved algorithm for various codes}
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\label{fig:prox:improved:comp}
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\label{fig:prox:improved:comp}
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\end{figure}
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\end{figure}
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@ -263,7 +263,7 @@ Figure \ref{fig:theo:tanner_graph} shows the Tanner graph for the
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\draw (cn3) -- (c7);
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\draw (cn3) -- (c7);
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\end{tikzpicture}
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\end{tikzpicture}
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\caption{Tanner graph for the (7,4)-Hamming-code}
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\caption{Tanner graph for the (7,4) Hamming code}
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\label{fig:theo:tanner_graph}
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\label{fig:theo:tanner_graph}
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\end{figure}%
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\end{figure}%
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%
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%
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