diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index b00db2e..2bb9f96 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/latex/thesis/chapters/decoding_techniques.tex @@ -199,6 +199,8 @@ of the \acp{LLR} $\gamma_i$ \cite[Sec. 2.5]{feldman_thesis}:% {f_{Y_i | C_i} \left( y_i \mid C_i = 1 \right) } \right) .\end{align*} % +\todo{$C_i$ or $c_i$?}% +% The authors propose the following cost function% \footnote{In this context, \textit{cost function} and \textit{objective function} have the same meaning.} @@ -208,6 +210,8 @@ for the \ac{LP} decoding problem:% g\left( \boldsymbol{c} \right) = \sum_{i=1}^{n} \gamma_i c_i .\end{align*} % +\todo{Write as dot product} +% With this cost function, the exact integer linear program formulation of \ac{ML} decoding is the following:% % @@ -234,6 +238,8 @@ decoding, redefining the constraints in terms of the \text{codeword polytope} \sum_{\boldsymbol{c} \in \mathcal{C}} \lambda_{\boldsymbol{c}} = 1 \right\} ,\end{align*} % % +\todo{$\lambda$ might be confusing here}% +% which represents the \textit{convex hull} of all possible codewords, i.e., the convex set of linear combinations of all codewords. This corresponds to simply lifting the integer requirement.