From 696e31ed249ea958e5a52757c07b21793042a4c7 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Thu, 13 Apr 2023 01:57:19 +0200 Subject: [PATCH] Added reference to the ML certificate property --- latex/thesis/chapters/lp_dec_using_admm.tex | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/latex/thesis/chapters/lp_dec_using_admm.tex b/latex/thesis/chapters/lp_dec_using_admm.tex index 0fc7bf5..b245e01 100644 --- a/latex/thesis/chapters/lp_dec_using_admm.tex +++ b/latex/thesis/chapters/lp_dec_using_admm.tex @@ -527,7 +527,14 @@ The resulting formulation of the relaxed optimization problem becomes% \end{aligned} \label{eq:lp:relaxed_formulation} \end{align}% -\todo{Mention ML certificate property} +One aspect making \ac{LP} decoding especially appealing is the very strong +theoretical guarantee that comes with it, called the +\textit{\ac{ML} certificate property} \cite[Sec. III. B.]{feldman_paper}. +This is the property that when a valid result is produced by an \ac{LP} +decoder, it is always the \ac{ML} codeword. +This leads to an interesting application of \ac{LP} decoding to +approximate \ac{ML} decoding behavior, by successively adding redundant +parity-checks until a valid result is returned \cite[Sec. IV.]{alp}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%