diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index 164767d..f10ab02 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/latex/thesis/chapters/decoding_techniques.tex @@ -770,7 +770,7 @@ The steps to solve the dual problem then become: % Luckily, the additional constaints only affect the $\boldsymbol{z}_j$-update steps. Furthermore, the $\boldsymbol{z}_j$-update steps can be shown to be equivalent to projections -onto the check polytopes $\mathcal{P}_{d_j}$ \cite[Sec. III. B.]{original_admm} +onto the check polytopes $\mathcal{P}_{d_j}$ and the $\tilde{\boldsymbol{c}}$-update can be computed analytically% % \footnote{In the $\tilde{c}_i$-update rule, the term @@ -780,7 +780,7 @@ What is actually meant is the component of $\boldsymbol{z}_j$ that is associated with the variable node $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}\boldsymbol{z}_j\right)_i$. The same is true for $\left( \boldsymbol{\lambda}_j \right)_i$.} % -\cite[Sec. III.]{lautern}:% +\cite[Sec. III. B.]{original_admm}:% % \begin{alignat*}{3} \tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left(