diff --git a/letter.tex b/letter.tex index b46a70d..9624d42 100644 --- a/letter.tex +++ b/letter.tex @@ -958,231 +958,232 @@ the code parameters, and the SNR. \printbibliography -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Response to the reviews -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% +% % +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % Response to the reviews +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % -\newpage -\onecolumn +% \newpage +% \onecolumn -\section{Authors' Response to the Editor resp. the Reviewers} +% \section{Authors' Response to the Editor resp. the Reviewers} -Before addressing the comments of the reviewers, the authors would first like to thank the editor and the reviewers for their tremendous efforts and their valuable comments which will help us to improve the paper. We hope that the upcoming changes meet your approval and address all the concerns. In the following section we respond to the comments of the reviews and mark the according changes in the paper. +% Before addressing the comments of the reviewers, the authors would first like to thank the editor and the reviewers for their tremendous efforts and their valuable comments which will help us to improve the paper. We hope that the upcoming changes meet your approval and address all the concerns. In the following section we respond to the comments of the reviews and mark the according changes in the paper. -\subsection{Editor} +% \subsection{Editor} -\begin{itemize} - \item \textbf{Comment 1:} [...] Your manuscript requires revisions, as outlined below, before the paper can be published. If these revisions are satisfactorily made (including meeting the length guidelines), the paper will be accepted for publication. [...] +% \begin{itemize} +% \item \textbf{Comment 1:} [...] Your manuscript requires revisions, as outlined below, before the paper can be published. If these revisions are satisfactorily made (including meeting the length guidelines), the paper will be accepted for publication. [...] - \vspace{0.25cm} - \textbf{Authors:} - Thank you for your positive feedback. The ``length-issue" stems from the fact that the submitted version has been compiled without the thanks and the acknowledgments. It should be solved by now. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for your positive feedback. The ``length-issue" stems from the fact that the submitted version has been compiled without the thanks and the acknowledgments. It should be solved by now. +% \vspace{0.75cm} - \item \textbf{Comment 2:} Reviewer 2 suggests to add some more simulations. +% \item \textbf{Comment 2:} Reviewer 2 suggests to add some more simulations. - \vspace{0.25cm} - \textbf{Authors:} - We added simulation results for different values of $N$, as the reviewer suggested. - Unfortunately, due to the short revision time and temporal constraints due to the - summer break, we were not able to add further results regarding the complexity and - different codes and parameters. -\end{itemize} +% \vspace{0.25cm} +% \textbf{Authors:} +% We added simulation results for different values of $N$, as the reviewer suggested. +% Unfortunately, due to the short revision time and temporal constraints due to the +% summer break, we were not able to add further results regarding the complexity and +% different codes and parameters. +% \end{itemize} -\subsection{Review 1} +% \subsection{Review 1} -\begin{itemize} - \item \textbf{Comment 1:} I believe that the paper deserves publication. I think the paper has been considerably improved. +% \begin{itemize} +% \item \textbf{Comment 1:} I believe that the paper deserves publication. I think the paper has been considerably improved. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for your positive feedback. We also would like to thank you for your insightful comments which helped to improve the paper. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for your positive feedback. We also would like to thank you for your insightful comments which helped to improve the paper. +% \vspace{0.75cm} - \item \textbf{Comment 2:} - A side note: I could not find the point-by-point letter of reply. Nevertheless, I could track the changes applied to the manuscript, for the issues I've pointed out in the first version of the manuscript. +% \item \textbf{Comment 2:} +% A side note: I could not find the point-by-point letter of reply. Nevertheless, I could track the changes applied to the manuscript, for the issues I've pointed out in the first version of the manuscript. - \vspace{0.25cm} - \textbf{Authors:} - That is strange; we uploaded the comments together with the revised version of the paper, coloring the added phrases according to the request of the reviews. - \vspace{.1cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% That is strange; we uploaded the comments together with the revised version of the paper, coloring the added phrases according to the request of the reviews. +% \vspace{.1cm} -\end{itemize} +% \end{itemize} -\subsection{Review 2} +% \subsection{Review 2} -\begin{itemize} - \item \textbf{Comment 1:} The authors have made substantial revisions to the manuscript based on the reviewers' feedback. Nevertheless, there are some issues that need to be addressed. +% \begin{itemize} +% \item \textbf{Comment 1:} The authors have made substantial revisions to the manuscript based on the reviewers' feedback. Nevertheless, there are some issues that need to be addressed. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for the positive assessment that several helpful changes have been made. We will address the remaining concerns in the following and add \reviewfour{according changes to the paper}. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for the positive assessment that several helpful changes have been made. We will address the remaining concerns in the following and add \reviewfour{according changes to the paper}. +% \vspace{0.75cm} - \item \textbf{Comment 2:} It seems that the PMF defined in Section II.A is not used. If not, delete it. +% \item \textbf{Comment 2:} It seems that the PMF defined in Section II.A is not used. If not, delete it. - \vspace{0.25cm} - \textbf{Authors:} - The according sentence has been removed. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% The according sentence has been removed. +% \vspace{0.75cm} - \item \textbf{Comment 3:} The definition of DFR is not provided. Decoding failure seems that the decoded result is not the valid codeword. +% \item \textbf{Comment 3:} The definition of DFR is not provided. Decoding failure seems that the decoded result is not the valid codeword. - \vspace{0.25cm} - \textbf{Authors:} - At the beginning of section III.A---upon introducing the abbreviation DFR---it is stated that ``[...] Hereby, a \emph{decoding failure} is defined as returning a \emph{non valid codeword}, i.e., as non-convergence of the algorithm. [...]" - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% At the beginning of section III.A---upon introducing the abbreviation DFR---it is stated that ``[...] Hereby, a \emph{decoding failure} is defined as returning a \emph{non valid codeword}, i.e., as non-convergence of the algorithm. [...]" +% \vspace{0.75cm} - \item \textbf{Comment 4:} In line 36 of page 3, ${c}'_i$ should be $c_{i’}$. +% \item \textbf{Comment 4:} In line 36 of page 3, ${c}'_i$ should be $c_{i’}$. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for noting this typo. The according equation has been corrected: +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for noting this typo. The according equation has been corrected: - \vspace{0.25cm} - ``[...] To reason this approach, Fig. \ref{fig:p_error} shows Monte Carlo simulations of the probability that the decoded bit \reviewfour{$\hat{c}_{i'}$} at position $i'$ of the estimated codeword is wrong. [...]" - \vspace{0.75cm} +% \vspace{0.25cm} +% ``[...] To reason this approach, Fig. \ref{fig:p_error} shows Monte Carlo simulations of the probability that the decoded bit \reviewfour{$\hat{c}_{i'}$} at position $i'$ of the estimated codeword is wrong. [...]" +% \vspace{0.75cm} - \item \textbf{Comment 5:} The values of $\gamma$, $\omega$ and $\eta$ used in this paper are identical to [11], which should be indicated in Section IV. +% \item \textbf{Comment 5:} The values of $\gamma$, $\omega$ and $\eta$ used in this paper are identical to [11], which should be indicated in Section IV. - \vspace{0.25cm} - \textbf{Authors:} - We added a short comment: +% \vspace{0.25cm} +% \textbf{Authors:} +% We added a short comment: - \vspace{0.25cm} - ``[...] They \reviewfour{adhere to \cite{proximal_paper} and} were determined to offer the best performance in a preliminary examination, - where the effect of changing multiple parameters was simulated over a wide - range of values. [...]" - \vspace{0.75cm} +% \vspace{0.25cm} +% ``[...] They \reviewfour{adhere to \cite{proximal_paper} and} were determined to offer the best performance in a preliminary examination, +% where the effect of changing multiple parameters was simulated over a wide +% range of values. [...]" +% \vspace{0.75cm} - \item \textbf{Comment 6:} $\gamma$, $\omega$ and $\eta$ are the parameters of proximal decoding. Are the values of these parameters optimal for list proximal decoding? The authors should provide some simulation results to illustrate the influence of changing these parameters on the performance of list proximal decoding. +% \item \textbf{Comment 6:} $\gamma$, $\omega$ and $\eta$ are the parameters of proximal decoding. Are the values of these parameters optimal for list proximal decoding? The authors should provide some simulation results to illustrate the influence of changing these parameters on the performance of list proximal decoding. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for this hint. In deed, these parameters were chosen since they are close-to-optimum for stand-alone proximal decoding and turned out to be at least well functioning for the improved list-based algorithm. Optimization of those values for the improved list-version has not been conducted up to now. This is subject to future research. To clarify, we added the following explanation: +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for this hint. In deed, these parameters were chosen since they are close-to-optimum for stand-alone proximal decoding and turned out to be at least well functioning for the improved list-based algorithm. Optimization of those values for the improved list-version has not been conducted up to now. This is subject to future research. To clarify, we added the following explanation: - \vspace{0.25cm} - ``[...] - The parameters chosen for the simulation are $\gamma = 0.05, \omega=0.05, \eta=1.5, K=200$ % - \reviewfour{as for proximal decoding, since those parameters also turned out close-to-optimum for as the improved algorithm in our simulations.} - [...]'' - \vspace{0.75cm} +% \vspace{0.25cm} +% ``[...] +% The parameters chosen for the simulation are $\gamma = 0.05, \omega=0.05, \eta=1.5, K=200$ % +% \reviewfour{as for proximal decoding, since those parameters also turned out close-to-optimum for as the improved algorithm in our simulations.} +% [...]'' +% \vspace{0.75cm} - \item \textbf{Comment 7:} $N$ is the main parameter for list proximal decoding. More simulation results with different $N$ should be provided. +% \item \textbf{Comment 7:} $N$ is the main parameter for list proximal decoding. More simulation results with different $N$ should be provided. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for the comment. Several analyses showed that $N=8$ is a very good compromise between effort resp. list size and performance. We added the following comment: +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for the comment. Several analyses showed that $N=8$ is a very good compromise between effort resp. list size and performance. We added the following comment: - \setcounter{table}{0} +% \setcounter{table}{0} - \vspace{0.25cm} - ``[...] - The number of possibly wrong components was selected as $N=8$. - \reviewfour{ - To reason this choice, Table \ref{N Table} shows the SNRs required for $N\in\{4, 6, 8, 10, 12\}$ to achieve an FER of $10^{-2}$ and $10^{-3}$, respectively. - } - \begin{table}[hbt] - \centering - \reviewfour{ - \caption{SNR (in dB) to achieve target FERs $10^{-2}$ and $10^{-3}$} - \label{N Table} - \begin{tabular}{c|ccccc} - $N$ & 4 & 6 & 8 & 10 & 12 \\ \hline - $\text{FER} = 10^{-2}$ & $4.94$ & $4.76$ & $4.67$ & $4.60$ & $4.54$ \\ - $\text{FER} = 10^{-3}$ & $5.84$ & $5.61$ & $5.49$ & $5.39$ & $5.32$ \\ - \end{tabular} - } - \end{table} - [...]" - \vspace{0.75cm} +% \vspace{0.25cm} +% ``[...] +% The number of possibly wrong components was selected as $N=8$. +% \reviewfour{ +% To reason this choice, Table \ref{N Table} shows the SNRs required for $N\in\{4, 6, 8, 10, 12\}$ to achieve an FER of $10^{-2}$ and $10^{-3}$, respectively. +% } +% \begin{table}[hbt] +% \centering +% \reviewfour{ +% \caption{SNR (in dB) to achieve target FERs $10^{-2}$ and $10^{-3}$} +% \label{N Table} +% \begin{tabular}{c|ccccc} +% $N$ & 4 & 6 & 8 & 10 & 12 \\ \hline +% $\text{FER} = 10^{-2}$ & $4.94$ & $4.76$ & $4.67$ & $4.60$ & $4.54$ \\ +% $\text{FER} = 10^{-3}$ & $5.84$ & $5.61$ & $5.49$ & $5.39$ & $5.32$ \\ +% \end{tabular} +% } +% \end{table} +% [...]" +% \vspace{0.75cm} - \item \textbf{Comment 8:} More simulation results with different $R$ should be provided, such as $R = 0.25$ and $R = 0.75$. +% \item \textbf{Comment 8:} More simulation results with different $R$ should be provided, such as $R = 0.25$ and $R = 0.75$. - \vspace{0.25cm} - \textbf{Authors:} - Unfortunately, due to the short revision time and temporal constraints due to the summer break as well as---even more important---the space constraint inherent to a letter, we were not able to add these results to the current paper. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% Unfortunately, due to the short revision time and temporal constraints due to the summer break as well as---even more important---the space constraint inherent to a letter, we were not able to add these results to the current paper. +% \vspace{0.75cm} - \item \textbf{Comment 9:} The iteration number of BP should be provided. +% \item \textbf{Comment 9:} The iteration number of BP should be provided. - \vspace{0.25cm} - \textbf{Authors:} - We added the number of iterations: +% \vspace{0.25cm} +% \textbf{Authors:} +% We added the number of iterations: - \vspace{0.25cm} - ``As shown in Fig. \ref{fig:results}, it can be seen that BP decoding \reviewfour{with $200$ iterations} outperforms the improved scheme by approximately $\SI{1.7}{dB}$. - [...]'' - \vspace{0.75cm} +% \vspace{0.25cm} +% ``As shown in Fig. \ref{fig:results}, it can be seen that BP decoding \reviewfour{with $200$ iterations} outperforms the improved scheme by approximately $\SI{1.7}{dB}$. +% [...]'' +% \vspace{0.75cm} - \item \textbf{Comment 10:} The complexity comparison among proximal decoding, list proximal decoding and BP should be provided. +% \item \textbf{Comment 10:} The complexity comparison among proximal decoding, list proximal decoding and BP should be provided. - \vspace{0.25cm} - \textbf{Authors:} Thank you for encouraging a more detailed comparison of according complexity. In our opinion, a more in-depth analysis would go beyond the space limitations of this letter, which primarily aims at describing the idea of improving proximal decoding by means of using a suitably defined list. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} Thank you for encouraging a more detailed comparison of according complexity. In our opinion, a more in-depth analysis would go beyond the space limitations of this letter, which primarily aims at describing the idea of improving proximal decoding by means of using a suitably defined list. +% \vspace{0.75cm} - \item \textbf{Comment 11:} In Section IV, the authors said “Nevertheless, note that Algorithm 2 requires only linear operations and could be favorable in applications as, e.g., massive MIMO, in which application of BP is prohibitive [11].”, but no simulation results support this conclusion. In [11], the proximal decoding has better performance than the BP decoding, which can not indicate that the proposed list proximal decoding also shows better performance for LDPC coded massive MIMO systems. +% \item \textbf{Comment 11:} In Section IV, the authors said “Nevertheless, note that Algorithm 2 requires only linear operations and could be favorable in applications as, e.g., massive MIMO, in which application of BP is prohibitive [11].”, but no simulation results support this conclusion. In [11], the proximal decoding has better performance than the BP decoding, which can not indicate that the proposed list proximal decoding also shows better performance for LDPC coded massive MIMO systems. - \vspace{0.25cm} - \textbf{Authors:} This is perfectly true. As of now, our comparison has been conducted for SISO systems only and it is not yet analyzed whether they carry over to (massive) MIMO systems. This sentence is directly based on \cite{proximal_paper} and had been added after the first review in order to motivate that the consideration of proximal decoding makes sense after all. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} This is perfectly true. As of now, our comparison has been conducted for SISO systems only and it is not yet analyzed whether they carry over to (massive) MIMO systems. This sentence is directly based on \cite{proximal_paper} and had been added after the first review in order to motivate that the consideration of proximal decoding makes sense after all. +% \vspace{0.75cm} - \item \textbf{Comment 12:} “Figure” and “Fig.” are mixed in this paper, such Figure 5 and Fig. 5. The authors should used unified representation. +% \item \textbf{Comment 12:} “Figure” and “Fig.” are mixed in this paper, such Figure 5 and Fig. 5. The authors should used unified representation. - \vspace{0.25cm} - \textbf{Authors:} Thank you for pointing out this inconsistency. We changed it to ``Fig.'' throughout the paper. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} Thank you for pointing out this inconsistency. We changed it to ``Fig.'' throughout the paper. +% \vspace{0.75cm} -\end{itemize} +% \end{itemize} -\subsection{Review 3} +% \subsection{Review 3} -\begin{itemize} - \item \textbf{Comment 1:} All my comments have been addressed carefully. I have no further comments. +% \begin{itemize} +% \item \textbf{Comment 1:} All my comments have been addressed carefully. I have no further comments. - \vspace{0.25cm} - \textbf{Authors:} - Thank you for your positive feedback. We also would like to thank you for your insightful comments which helped to improve the paper. - \vspace{0.75cm} +% \vspace{0.25cm} +% \textbf{Authors:} +% Thank you for your positive feedback. We also would like to thank you for your insightful comments which helped to improve the paper. +% \vspace{0.75cm} -\end{itemize} +% \end{itemize} \end{document} +