From 0d9a40e894ed64fba2f166988d145098c881fa84 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Mon, 20 Feb 2023 08:54:52 +0100 Subject: [PATCH] Wording changes to LP decoding --- latex/thesis/chapters/decoding_techniques.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index 6d27d76..5811f68 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/latex/thesis/chapters/decoding_techniques.tex @@ -173,7 +173,7 @@ representation. To solve the resulting linear program, various optimization methods can be used. -Feldman et al. begin by looking at the \ac{ML} decoding problem% +They begin by looking at the \ac{ML} decoding problem% \footnote{They assume that all codewords are equally likely to be transmitted, making the \ac{ML} and \ac{MAP} decoding problems equivalent.}% % @@ -220,8 +220,8 @@ Especially for the continuous variable in LP decoding} As solving integer linear programs is generally NP-hard, this decoding problem has to be approximated by one with looser constraints. A technique called \textit{relaxation} is applied: -modifying the constraints in order to broaden the considered -domain (e.g. by lifting the integer requirement). +relaxing the constraints, thereby broadening the considered domain +(e.g. by lifting the integer requirement). First, the authors present an equivalent \ac{LP} formulation of exact \ac{ML} decoding, redefining the constraints in terms of the \text{codeword polytope} % @@ -275,7 +275,7 @@ feasible solutions. Figure \ref{fig:dec:poly:local} shows the local codeword polytope of each check node. Their intersection, the relaxed codeword polytope $\overline{Q}$, is shown in -figure \ref{fig:dec:poly:relaxed}. +figure \ref{fig:dec:poly:relaxed}.% % % %