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Minor wording and formatting changes

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Andreas Tsouchlos 2023-04-09 23:21:18 +02:00
parent 7af0eaea5b
commit 65214feb01
1 changed files with 8 additions and 5 deletions
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13
latex/thesis/chapters/proximal_decoding.tex
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@ -228,7 +228,7 @@ $\Pi_{\eta}\left( \cdot \right) $ expressing the projection onto
$\left[ -\eta, \eta \right]^n$.
The iterative decoding process resulting from these considerations is
summarized in algorithm \ref{alg:prox}.
depicted in algorithm \ref{alg:prox}.
\begin{genericAlgorithm}[caption={Proximal decoding algorithm for an \ac{AWGN} channel},
label={alg:prox}]
@ -1317,7 +1317,7 @@ most likely candidate.
This process is outlined in algorithm \ref{alg:prox:improved}.
Its only difference to algorithm \ref{alg:prox} is that instead of returning
the last estimate when no valid result is reached, an ML-in-the-List step is
performed (highlighted in blue).
performed.
\begin{genericAlgorithm}[caption={Improved proximal decoding algorithm},
label={alg:prox:improved},]
@ -1331,9 +1331,12 @@ for $K$ iterations do
end if
end for
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_i\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified}}$
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\tilde{c}}_i}$
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_i\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right)}$
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_l,\hspace{1mm}
l\in [1:n]\text{ of } \boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified}}$
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_l,
\boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\tilde{c}}_l}$
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_l\text{ with lowest }
d_H\left( \boldsymbol{ \tilde{c}}_l, \boldsymbol{\hat{c}} \right)}$
\end{genericAlgorithm}
\todo{Not hamming distance, correlation}