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§Minor wording changes

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Andreas Tsouchlos 2023-02-19 14:45:04 +01:00
parent c1473c6eb4
commit 8880423d1e
1 changed files with 4 additions and 4 deletions
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latex/thesis/chapters/decoding_techniques.tex
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@ -578,7 +578,7 @@ The resulting formulation of the relaxed optimization problem is the following:%
\end{subfigure} \end{subfigure}
\caption{Visualization of the codeword polytope and the relaxed codeword \caption{Visualization of the codeword polytope and the relaxed codeword
polytope for an example code} polytope}
\label{fig:dec:poly} \label{fig:dec:poly}
\end{figure}% \end{figure}%
% %
@ -651,7 +651,7 @@ the so-called \textit{code-constraint polynomial} is introduced:%
.\end{align*}% .\end{align*}%
% %
The intention of this function is to provide a way to penalize vectors far The intention of this function is to provide a way to penalize vectors far
from a codeword and favor those close to a codeword. from a codeword and favor those close to one.
In order to achieve this, the polynomial is composed of two parts: one term In order to achieve this, the polynomial is composed of two parts: one term
representing the bipolar constraint, providing for a discrete solution of the representing the bipolar constraint, providing for a discrete solution of the
continuous optimization problem, and one term representing the parity continuous optimization problem, and one term representing the parity
@ -781,7 +781,7 @@ it suffices to consider only proportionality instead of equality.}%
&\propto \boldsymbol{x} - \boldsymbol{y} &\propto \boldsymbol{x} - \boldsymbol{y}
,\end{align*}% ,\end{align*}%
% %
Allowing equation \ref{eq:prox:step_log_likelihood} to be rewritten as% allowing equation \ref{eq:prox:step_log_likelihood} to be rewritten as%
% %
\begin{align*} \begin{align*}
\boldsymbol{r} \leftarrow \boldsymbol{s} \boldsymbol{r} \leftarrow \boldsymbol{s}
@ -823,6 +823,6 @@ return $\boldsymbol{\hat{c}}$
\end{genericAlgorithm} \end{genericAlgorithm}
\caption{Proximal decoding algorithm} \caption{Proximal decoding algorithm for an \ac{AWGN} channel}
\label{fig:prox:alg} \label{fig:prox:alg}
\end{figure} \end{figure}