From fc06ec952f5efefc3e3f8474d166f109868c90db Mon Sep 17 00:00:00 2001 From: Steven Franke Date: Mon, 28 Dec 2015 03:02:05 +0000 Subject: [PATCH] Edits to section 1 and corrections to n-k+1 stuff. git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6321 ab8295b8-cf94-4d9e-aec4-7959e3be5d79 --- lib/ftrsd/ftrsd_paper/fig_wer3.gnuplot | 22 +++++----- lib/ftrsd/ftrsd_paper/ftdata-10000.dat | 6 +-- lib/ftrsd/ftrsd_paper/ftdata-100000.dat | 4 +- lib/ftrsd/ftrsd_paper/ftrsd.lyx | 57 +++++++++++++++---------- 4 files changed, 49 insertions(+), 40 deletions(-) diff --git a/lib/ftrsd/ftrsd_paper/fig_wer3.gnuplot b/lib/ftrsd/ftrsd_paper/fig_wer3.gnuplot index 4f87d29d2..f066179ac 100644 --- a/lib/ftrsd/ftrsd_paper/fig_wer3.gnuplot +++ b/lib/ftrsd/ftrsd_paper/fig_wer3.gnuplot @@ -1,19 +1,17 @@ -# gnuplot script for AWGN vs Rayleigh figure +# gnuplot script for "Percent copy" figure +# run: gnuplot fig_wer3.gnuplot +# then: pdflatex fig_wer3.tex # -set term epslatex standalone size 16cm,8cm +set term epslatex standalone size 6in,6*2/3in set output "fig_wer3.tex" -set xlabel "$E_s/N_o$ (dB)" -set ylabel "WER" +set xlabel "SNR in 2500 Hz Bandwidth (dB)" +set ylabel "Percent Copy" set style func linespoints -set key on top outside nobox +set key off set tics in set mxtics 2 set mytics 10 set grid -set logscale y -#set format y "10^{%L}" -plot "ftdata-1000-rf.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 7 title "FT-1K-RF", \ -"ftdata-10000-rf.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 7 title "FT-10K-RF", \ -"bmdata-rf.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 5 title 'BM-RF', \ -"ftdata-10000.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 7 title 'FT-10K-AWGN', \ -"bmdata.dat" using ($1+29.7):(1-$2) with linespoints pt 5 title 'BM-AWGN' +plot [-27:-22] [0:110] \ + "ftdata-100000.dat" using 1:(100*$3) with linespoints lt 1 pt 7 title 'FT-100K', \ + "ftdata-100000.dat" using 1:(100*$2) with linespoints lt 1 pt 7 title 'FT-100K' diff --git a/lib/ftrsd/ftrsd_paper/ftdata-10000.dat b/lib/ftrsd/ftrsd_paper/ftdata-10000.dat index 0c42e9336..54480ff45 100644 --- a/lib/ftrsd/ftrsd_paper/ftdata-10000.dat +++ b/lib/ftrsd/ftrsd_paper/ftdata-10000.dat @@ -1,9 +1,9 @@ snr psuccess ntrials 10000 r6315 -26.5 0.004 x -26.0 0.03 x --25.5 0.107 --25.0 0.353 --24.5 0.653 +-25.5 0.107 0.19 +-25.0 0.353 0.40 (2) +-24.5 0.653 -24.0 0.913 -23.5 0.983 -23.0 0.9987 x diff --git a/lib/ftrsd/ftrsd_paper/ftdata-100000.dat b/lib/ftrsd/ftrsd_paper/ftdata-100000.dat index b0bdce3f5..744eecf7d 100644 --- a/lib/ftrsd/ftrsd_paper/ftdata-100000.dat +++ b/lib/ftrsd/ftrsd_paper/ftdata-100000.dat @@ -2,9 +2,9 @@ snr psuccess 100000 trials r6315 -27.0 0.0 x -26.5 0.007 x -26.0 0.057 --25.5 0.207 +-25.5 0.207 0.35 -25.0 0.531 0.67 --24.5 0.822 +-24.5 0.822 0.878 -24.0 0.953 -23.5 0.99423 -23.0 0.99967 302956/303056 diff --git a/lib/ftrsd/ftrsd_paper/ftrsd.lyx b/lib/ftrsd/ftrsd_paper/ftrsd.lyx index 73c2e23a6..41424baee 100644 --- a/lib/ftrsd/ftrsd_paper/ftrsd.lyx +++ b/lib/ftrsd/ftrsd_paper/ftrsd.lyx @@ -127,18 +127,27 @@ The following paragraph may not belong here - feel free to get rid of it, \end_layout \begin_layout Standard -The Franke-Taylor (FT) decoder described herein is a probabilistic list-decoder - that has been optimized for use in the short block-length, low-rate Reed-Solomo -n code used in JT65. - The particular approach that we have developed has a number of desirable +The Franke-Taylor (FT) decoder is a probabilistic list-decoder that we have + developed for use in the short block-length, low-rate Reed-Solomon code + used in JT65. + JT65 provides a unique sandbox for playing with decoding algorithms. + Several seconds are available for decoding a single 63-symbol message. + This is a long time! The luxury of essentially unlimited time allows us + to experiment with decoders that have high computational complexity. + The payoff is that we can extend the decoding threshold by many dB over + the hard-decision, Berlekamp-Massey decoder on a typical fading channel, + and by a meaningful amount over the KV decoder, long considered to be the + best available soft-decision decoder. + In addition to its excellent performance, the FT algorithm has other desirable properties, not the least of which is its conceptual simplicity. - The decoding performance and complexity scale in a useful way, providing - steadily increasing soft-decision decoding gain as a tunable computational - complexity parameter is increased over more than 5 orders of magnitude. - The fact that the algorithm requires a large number of independent decoding - trials should also make it possible to obtain significant performance gains - through parallelization. - + Decoding performance and complexity scale in a useful way, providing steadily + increasing soft-decision decoding gain as a tunable computational complexity + parameter is increased over more than 5 orders of magnitude. + This means that appreciable gain should be available from our decoder even + on very simple (and slow) computers. + On the other hand, because the algorithm requires a large number of independent + decoding trials, it should be possible to obtain significant performance + gains through parallelization on high-performance computers. \end_layout \begin_layout Section @@ -378,14 +387,16 @@ probabilistic decoding methods \begin_inset CommandInset citation LatexCommand cite +after "Chapter 10" key "key-1" \end_inset . - These algorithms generally involve some amount of educating guessing about - which received symbols are in error. - The guesses are informed by quality metrics, also known as + Such algorithms involve some amount of educating guessing about which received + symbols are in error or, alternatively, about which received symbols are + correct. + The guesses are informed by \begin_inset Quotes eld \end_inset @@ -393,11 +404,11 @@ soft-symbol \begin_inset Quotes erd \end_inset - metrics, associated with the received symbols. + quality metrics associated with the received symbols. To illustrate why it is absolutely essential to use such soft-symbol informatio -n to identify symbols that are most likely to be in error it helps to consider - what would happen if we tried to use completely random guesses, ignoring - any available soft-symbol information. +n in these algorithms it helps to consider what would happen if we tried + to use completely random guesses, ignoring any available soft-symbol informatio +n. \end_layout \begin_layout Standard @@ -997,11 +1008,11 @@ The correct JT65 codeword produces a value for bins containing both signal and noise power. Incorrect codewords have at most -\begin_inset Formula $k=12$ +\begin_inset Formula $k-1=11$ \end_inset such bins and at least -\begin_inset Formula $n-k=51$ +\begin_inset Formula $n-k+1=52$ \end_inset bins containing noise only. @@ -1033,7 +1044,7 @@ d-deviation uncertainty range assumes Gaussian statistics. \begin_layout Standard \begin_inset Formula \[ -u=\frac{n-k\pm\sqrt{n-k}}{n}+\frac{k\pm\sqrt{k}}{n}(1+y). +u=\frac{n-k+1\pm\sqrt{n-k+1}}{n}+\frac{k-1\pm\sqrt{k-1}}{n}(1+y). \] \end_inset @@ -1044,7 +1055,7 @@ For JT65 this expression evaluates to \begin_layout Standard \begin_inset Formula \[ -u\approx1\pm0.13+(0.19\pm0.06)\, y. +u\approx1\pm0.11+(0.17\pm0.05)\, y. \] \end_inset @@ -1068,7 +1079,7 @@ As a specific example, consider signal strength \end_inset 0.6, while incorrect codewords will give -\begin_inset Formula $u\approx2.0\pm0.3$ +\begin_inset Formula $u\approx1.7\pm0.3$ \end_inset or less.