Added todos

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Andreas Tsouchlos 2023-03-17 00:33:59 +01:00
parent 4643a77973
commit d333e461a7

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@ -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.