From 1632c0744e525f5e23705c4fcbd9ac63570b786d Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sun, 9 Apr 2023 02:40:46 +0200 Subject: [PATCH] Wrote introduction to improved implementation --- latex/thesis/chapters/proximal_decoding.tex | 26 ++++++++++----------- 1 file changed, 13 insertions(+), 13 deletions(-) diff --git a/latex/thesis/chapters/proximal_decoding.tex b/latex/thesis/chapters/proximal_decoding.tex index bde076c..90c522e 100644 --- a/latex/thesis/chapters/proximal_decoding.tex +++ b/latex/thesis/chapters/proximal_decoding.tex @@ -505,6 +505,8 @@ the decoding performance when keeping the value within a reasonable window (''slightly larger than one``, as stated in \cite[Sec. 3.2]{proximal_paper}), which seems plausible considering its only function is ensuring numerical stability. +Summarizing the above considerations, \ldots + \begin{itemize} \item Conclusion: Number of iterations independent of \ac{SNR} \end{itemize} @@ -1234,22 +1236,20 @@ returning an invalid codeword. \section{Improved Implementation}% \label{sec:prox:Improved Implementation} +As mentioned earlier, frame errors seem to mainly stem from decoding failures. +This, coupled with the fact that the \ac{BER} indicates so much better +performance than the \ac{FER}, leads to the assumption that only a small +number of components of the estimated vector may be responsible for an invalid +result. +If it was possible to limit the number of possibly wrong components of the +estimate to a small subset, an \ac{ML}-decoding step could be performed on +a limited number of possible results (``ML-in-the-List'' as it will +subsequently be called) to improve the decoding performance. +This concept is pursued in this section. + \begin{itemize} - \item Improvement using ``ML-on-List'' - \begin{itemize} - \item Attach to FER problem - \item - \end{itemize} \item Decoding performance and comparison with standard proximal decoding - \begin{itemize} - \item asdf - \item ghjk - \end{itemize} \item Computational performance and comparison with standard proximal decoding - \begin{itemize} - \item asdf - \item ghjk - \end{itemize} \item Conclusion \begin{itemize} \item Summary