Added citations for different methods to solve lp decoding problem

latex/thesis/chapters/decoding_techniques.tex

@@ -175,8 +175,8 @@ which minimizes the objective function $g$.
 decoding and one, which is an approximation with a more manageable
 representation.
 To solve the resulting linear program, various optimization methods can be
-used.
-\todo{Citation needed}
+used (see for example \cite{alp}, \cite{interior_point},
+\cite{efficient_lp_dec_admm}, \cite{pdd}).
 
 They begin by looking at the \ac{ML} decoding problem%
 \footnote{They assume that all codewords are equally likely to be transmitted,
@@ -685,7 +685,6 @@ The resulting formulation of the relaxed optimization problem becomes:%
         \hspace{5mm}\forall j\in\mathcal{J}.
     \end{aligned} \label{eq:lp:relaxed_formulation}
 \end{align}%
-\todo{Space before $\forall$?}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -730,7 +729,6 @@ In this form, the problem almost fits the \ac{ADMM} template described in sectio
 \ref{sec:theo:Optimization Methods}, except for the fact that there are multiple equality
 constraints $\boldsymbol{T}_j \tilde{\boldsymbol{c}} = \boldsymbol{z}_j$ and the
 additional constraints $\boldsymbol{z}_j \in \mathcal{P}_{d_j} \, \forall\, j\in\mathcal{J}$.
-\todo{$\forall$ in text?}
 The multiple constraints can be addressed by introducing additional terms in the
 augmented lagrangian:%
 %
@@ -830,7 +828,6 @@ able to be handled at the same time.
 This can also be understood by interpreting the decoding process as a message-passing
 algorithm \cite[Sec. III. D.]{original_admm}, \cite[Sec. II. B.]{efficient_lp_dec_admm},
 as is shown in figure \ref{fig:lp:message_passing}.%
-\todo{Explicitly specify sections?}%
 %
 \begin{figure}[H]
     \centering