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Fixed i, j notation in proximal decoding explanation

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This commit is contained in:
Andreas Tsouchlos 2023-03-09 12:23:13 +01:00
parent d4dc490e49
commit eceda0b50f
2 changed files with 5 additions and 5 deletions
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8
latex/thesis/chapters/decoding_techniques.tex
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@ -743,10 +743,10 @@ the so-called \textit{code-constraint polynomial} is introduced as:%
% %
\begin{align*} \begin{align*}
h\left( \boldsymbol{x} \right) = h\left( \boldsymbol{x} \right) =
\underbrace{\sum_{j=1}^{n} \left( x_j^2-1 \right) ^2}_{\text{Bipolar constraint}} \underbrace{\sum_{i=1}^{n} \left( x_i^2-1 \right) ^2}_{\text{Bipolar constraint}}
+ \underbrace{\sum_{i=1}^{m} \left[ + \underbrace{\sum_{j=1}^{m} \left[
\left( \prod_{j\in \mathcal{A} \left( \prod_{i\in N \left( j \right) } x_i \right)
\left( i \right) } x_j \right) -1 \right] ^2}_{\text{Parity constraint}}% -1 \right] ^2}_{\text{Parity constraint}}%
.\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

2
latex/thesis/chapters/theoretical_background.tex
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@ -83,7 +83,7 @@ Lastly, the optimization methods utilized are described.
\begin{itemize} \begin{itemize}
\item Introduction \item Introduction
\item Binary linear codes \item Binary linear codes
\item \Ac{LDPC} codes (especially $i$, $j$, parity check matrix $\boldsymbol{H}$, etc.) \item \Ac{LDPC} codes (especially $i$, $j$, parity check matrix $\boldsymbol{H}$, $N\left( j \right) $ \& $N\left( i \right) $, etc.)
\end{itemize} \end{itemize}