From 65214feb0141ce31ca9da1df3059d7bab8dd9ed2 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sun, 9 Apr 2023 23:21:18 +0200 Subject: [PATCH] Minor wording and formatting changes --- latex/thesis/chapters/proximal_decoding.tex | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/latex/thesis/chapters/proximal_decoding.tex b/latex/thesis/chapters/proximal_decoding.tex index e0d7246..1461e12 100644 --- a/latex/thesis/chapters/proximal_decoding.tex +++ b/latex/thesis/chapters/proximal_decoding.tex @@ -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}