More refinements to section 7 and figs.

git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6317 ab8295b8-cf94-4d9e-aec4-7959e3be5d79

lib/ftrsd/ftrsd_paper/fig_bodide.gnuplot

@@ -2,9 +2,9 @@
 # run: gnuplot fig_bodide.gnuplot
 # then: pdflatex fig_bodide.tex
 #
-set term epslatex standalone size 6in,4in
+set term epslatex standalone size 6in,2*6/3in
 set output "fig_bodide.tex"
-set xlabel "$E_s/N_0$ (dB)"
+set xlabel "$E_b/N_0$ (dB)"
 set ylabel "Word Error Rate"
 set style func linespoints
 set key off
@@ -13,8 +13,9 @@ set mxtics 2
 set mytics 10 
 set grid
 set logscale y
-plot [3:9] [1e-4:1] "bmdata.dat" using ($1+29.66):(1-$2) with linespoints pt 4 title 'BM', \
+plot [3:9] [1e-4:1] "bmdata.dat" using ($1+29.1):(1-$2) with linespoints lt 1 pt 4 title 'BM', \
-           "bmtheory25.dat" using 1:3 with linespoints pt 5 title 'theory25', \
+           "bmtheory25.dat" using ($1-0.6):3 with linespoints lt 2 pt 5 title 'theory25', \
-           "bmtheory40.dat" using 1:3 with linespoints pt 5 title 'theory40', \
+           "ftdata-100000.dat" using ($1+29.1):(1-$2) every ::1 with linespoints lt 1 pt 4 title 'FT', \
-           "bmtheory43.dat" using 1:3 with linespoints pt 5 title 'theory43', \
+           "kvasd-15.dat" using ($1+29.1):(1-$2) every ::1 with linespoints lt 1 pt 4 title 'KV', \
-           "ftdata-100000.dat" using ($1+29.66):(1-$2) every ::1 with linespoints pt 4 title 'FT'
+           "bodide.lab" with labels
+

lib/ftrsd/ftrsd_paper/fig_ntrials_vs_nhard.gnuplot

@@ -2,15 +2,14 @@
 # run: gnuplot fig_ntrials_vs_nhard.gnuplot
 # then: pdflatex fig_ntrials_vs_nhard.tex
 #
-set term epslatex standalone size 12cm,8cm
+set term epslatex standalone size 6in,2*6/3in
 set output "fig_ntrials_vs_nhard.tex"
 set xlabel "Errors in received word ($X$)"
 set ylabel "Number of trials"
-set title "AWGN, $\\frac{E_s}{N_o}=5.7$ dB"
+set title "AWGN, $\\frac{E_b}{N_o}=5.1$ dB"
 set tics in
 set mxtics 5
 set mytics 10
 #set grid
 set logscale y
 plot "stats-100000-24db-3.dat" using 1:4 pt 12 notitle
-#plot "stats-100000-24db-3.dat" using 1:4 pt 13 notitle

lib/ftrsd/ftrsd_paper/fig_wer2.gnuplot

@@ -2,7 +2,7 @@
 # run: gnuplot fig_wer2.gnuplot
 # then: pdflatex fig_wer2.tex
 #
-set term epslatex standalone size 5in,5*2/3in
+set term epslatex standalone size 6in,6*2/3in
 set output "fig_wer2.tex"
 set xlabel "SNR in 2500 Hz Bandwidth (dB)"
 set ylabel "Percent Copy"
@@ -17,8 +17,6 @@ plot [-27:-22] [0:110] \
      "ftdata-10000.dat" using 1:(100*$2) with linespoints lt 1 pt 7 title 'FT-10K', \
      "ftdata-1000.dat" using 1:(100*$2) with linespoints lt 1 pt 7 title 'FT-1K', \
      "ftdata-100.dat" using 1:(100*$2) with linespoints lt 1 pt 7 title 'FT-100', \
-     "kvasd-8.dat" using 1:(100*$2) with linespoints lt 2 pt 8 title 'KV-8', \
-     "kvasd-12.dat" using 1:(100*$2) with linespoints lt 2 pt 8 title 'KV-12', \
      "kvasd-15.dat" using 1:(100*$2) with linespoints lt 2 pt 8 title 'KV-15', \
      "bmdata.dat" using 1:(100*$2) with linespoints pt 11 title 'BM', \
      "wer2.lab" with labels

lib/ftrsd/ftrsd_paper/ftrsd.lyx

@@ -2,7 +2,7 @@
 \lyxformat 474
 \begin_document
 \begin_header
-\textclass article
+\textclass paper
 \use_default_options true
 \maintain_unincluded_children false
 \language english
@@ -84,6 +84,15 @@ Steven J.
  Taylor, K1JT
 \end_layout
 
+\begin_layout Standard
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Abstract
 The JT65 protocol has revolutionized amateur-radio weak-signal communication
  by enabling amateur radio operators with small antennas and relatively
@@ -333,7 +342,16 @@ Statistical Framework
 The FT algorithm uses the estimated quality of received symbols to generate
  lists of symbols considered likely to be in error, thus enabling decoding
  of received words with more than 25 errors.
- As a specific example, consider a received JT65 word with 23 correct symbols
+ 
+\end_layout
+
+\begin_layout Standard
+(SF: provide brief overview of literature survey and discuss the inspiration
+ for the FT approach).
+\end_layout
+
+\begin_layout Standard
+As a specific example, consider a received JT65 word with 23 correct symbols
  and 40 errors.
  We do not know which symbols are in error.
  Suppose that the decoder randomly selects 
@@ -738,7 +756,7 @@ The FT algorithm uses quality indices made available by a noncoherent 64-FSK
 \begin_inset Formula $p_{1}$
 \end_inset
 
-and 
+ and 
 \begin_inset Formula $p_{2}$
 \end_inset
 
@@ -1129,7 +1147,7 @@ Hinted Decoding
 \end_layout
 
 \begin_layout Standard
-Write this...
+To be written...
 \end_layout
 
 \begin_layout Section
@@ -1143,7 +1161,7 @@ Implementation in WSJT-X
 \end_layout
 
 \begin_layout Standard
-Write this...
+To be written...
 \end_layout
 
 \begin_layout Section
@@ -1153,75 +1171,84 @@ name "sec:Theory,-Simulation,-and"
 
 \end_inset
 
-Decoder Performance Evaluation: Simulations and Real Data
+Decoder Performance Evaluation
+\end_layout
+
+\begin_layout Subsection
+Simulated results on the AWGN channel
 \end_layout
 
 \begin_layout Standard
-The fraction of time that 
+Comparisons of decoding performance are usually presented in the professional
-\begin_inset Formula $X$
+ literature as plots of word error-rate versus 
+\begin_inset Formula $E_{b}/N_{0}$
 \end_inset
 
-, the number of symbols received incorrectly, is expected to be less than
+, the ratio of the energy collected per information bit to the one-sided
- some number 
+ noise power spectral density, 
-\begin_inset Formula $D$
+\begin_inset Formula $N_{0}$
 \end_inset
 
- depends on signal-to-noise ratio.
+.
- For the case of additive white Gaussian noise (AWGN) and noncoherent 64-FSK
+ In amateur radio circles performance is usually plotted as the probability
- demodulation this probability is easy to calculate.
+ of successfully decoding a received word vs signal-to-noise ratio in a
- Representative examples for 
+ 2.5 kHz reference bandwidth, 
-\begin_inset Formula $D=25,$
+\begin_inset Formula $\mathrm{SNR}{}_{2.5\,\mathrm{kHz}}$
 \end_inset
 
- 
+.
-\family roman
+ The relationship between 
-\series medium
+\begin_inset Formula $E_{b}/N_{o}$
-\shape up
-\size normal
-\emph off
-\bar no
-\strikeout off
-\uuline off
-\uwave off
-\noun off
-\color none
-
-\begin_inset Formula $D=40$
 \end_inset
 
-
+ and 
-\family default
+\begin_inset Formula $\mathrm{SNR}{}_{2.5\,\mathrm{kHz}}$
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\strikeout default
-\uuline default
-\uwave default
-\noun default
-\color inherit
-, and 
-\begin_inset Formula $D=43$
 \end_inset
 
- are plotted in Figure 
+ is described in Appendix 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Appendix:SNR"
+
+\end_inset
+
+.
+ 
+\end_layout
+
+\begin_layout Standard
+Results of simulations using the BM, FT, and KV decoding algorithms on the
+ JT65 (63,12) code are presented in terms of word error-rate vs 
+\begin_inset Formula $E_{b}/N_{o}$
+\end_inset
+
+ in Figure 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "fig:bodide"
 
 \end_inset
 
- for a range of SNRs as filled squares with connecting lines.
+.
- The rightmost such curve shows that on the AWGN channel the hard-decision
+ For these tests we generated at least 1000 signals at each signal-to-noise
- BM decoder should succeed about 90% of the time at 
+ ratio, assuming the additive white gaussian noise (AWGN) channel, and processed
-\begin_inset Formula $E_{s}/N_{0}=7.5$
+ the data using each algorithm.
+ For word error-rates less than 0.1 it was necessary to process 10,000 or
+ even 100,000 simulated signals in order to capture enough errors to make
+ the estimates of word-error-rate statistically meaningful.
+ As a test of the fidelity of our numerical simulations, Figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:bodide"
+
 \end_inset
 
- dB, 99% of the time at 8 dB, and 99.98% at 8.5 dB.
+ also shows theoretical results (filled squares) for comparison with the
- For comparison, the righmost curve with open squares shows that simulated
+ BM results.
- results agree with theory to within less than 0.2 dB.
+ The simulated BM results agree with theory to within about 0.1 dB.
- 
+ As expected, the soft-decision algorithms FT and KV are about 2 dB better
+ than the hard-decision BM algorithm.
+ In addition, FT has a slight edge (about 0.2 dB) over KV.
 \end_layout
 
 \begin_layout Standard
@@ -1248,56 +1275,33 @@ name "fig:bodide"
 \end_inset
 
 Word error rates as a function of 
-\begin_inset Formula $E_{s}/N_{0},$
+\begin_inset Formula $E_{b}/N_{0},$
 \end_inset
 
- the signal-to-noise ratio in bandwidth equal to the symbol rate.
+ the signal-to-noise ratio per bit.
- Filled squares illustrate theoretical values for 
+ The single curve marked with filled squares shows a theoretical prediction
-\begin_inset Formula $D=25,$
+ for the BM decoder.
-\end_inset
+ Open squares illustrate simulation results for an AWGN channel with the
-
+ BM, FT (
- 
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\strikeout off
-\uuline off
-\uwave off
-\noun off
-\color none
-
-\begin_inset Formula $D=40$
-\end_inset
-
-
-\family default
-\series default
-\shape default
-\size default
-\emph default
-\bar default
-\strikeout default
-\uuline default
-\uwave default
-\noun default
-\color inherit
-, and 
-\begin_inset Formula $D=43$
-\end_inset
-
-.
- Open squares illustrate measured results for the BM and FT (
 \begin_inset Formula $T=10^{5}$
 \end_inset
 
-) decoders in program 
+) and KV (
+\begin_inset Formula $\lambda=15$
+\end_inset
+
+) decoders used in program 
 \emph on
 WSJT-X
 \emph default
 .
+ The KV results are for decoding complexity coefficient 
+\begin_inset Formula $\lambda=15$
+\end_inset
+
+, the most aggressive setting that has historically been used in earlier
+ versions of the WSJT programs.
+ 
 \end_layout
 
 \end_inset
@@ -1311,38 +1315,170 @@ WSJT-X
 \end_layout
 
 \begin_layout Standard
-Received JT65 words with more than 25 incorrect symbols can be decoded if
+Because of the importance of error-free transmission in commercial applications,
- sufficient information on individual symbol reliabilities is available.
+ plots like that in Figure 
- Using values of 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:bodide"
+
+\end_inset
+
+ often extend downward to much smaller error rates, say 
+\begin_inset Formula $10^{-6}$
+\end_inset
+
+ or less.
+ The circumstances for minimal amateur-radio QSOs are very different, however.
+ Error rates of order 0.1 or higher may be acceptable.
+ In this case the essential information is better presented in a plot showing
+ the percentage of transmissions copied correctly as a function of signal-to-noi
+se ratio.
+ Figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:WER2"
+
+\end_inset
+
+ shows the FT results for 
+\begin_inset Formula $T=10^{5}$
+\end_inset
+
+ and the KV results that were shown in Figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:bodide"
+
+\end_inset
+
+ in this format along with additional FT results for 
+\begin_inset Formula $T=10^{4},10^{3},$
+\end_inset
+
+ and 
+\begin_inset Formula $10^{2}$
+\end_inset
+
+.
+ The KV results are plotted with open triangles.
+ It is apparent that the FT algorithm produces more decodes than KV when
+ 
+\begin_inset Formula $T=10^{4}$
+\end_inset
+
+ or larger.
+ 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+	filename fig_wer2.pdf
+	lyxscale 120
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:WER2"
+
+\end_inset
+
+Percent of JT65 messages copied as a function of SNR in 2.5 kHz bandwidth.
+ Solid lines with filled round circles are results from the FT decoder with
+ 
+\begin_inset Formula $T=10^{5},10^{4},10^{3},$
+\end_inset
+
+ and 
+\begin_inset Formula $10^{2}$
+\end_inset
+
+, respectively, from left to right.
+ The dashed line with open triangles is the KV decoder with complexity coefficie
+nt 
+\begin_inset Formula $\lambda=15$
+\end_inset
+
+.
+ Results from the BM algorithm are also shown with filled triangles.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The timeout parameter 
 \begin_inset Formula $T$
 \end_inset
 
- that are practical with today's personal computers and the soft-symbol
+ employed in the FT algorithm is the maximum number of symbol-erasure trials
- information described above, we find that the FT algorithm nearly always
+ allowed for a particular attempt at decoding a received word.
- produces correct decodes up to 
+ Most successful decodes take only a small fraction of the maximum allowed
-\begin_inset Formula $X=40$
+ number of trials.
-\end_inset
+ Figure 
-
-, and some additional decodes are found in the range 41 to 43.
- As an example, Figure 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "fig:N_vs_X"
 
 \end_inset
 
- plots the number of stochastic erasure trials required to find the correct
+ shows the number of stochastic erasure trials required to find the correct
- codeword versus the number of hard-decision errors for a run with 1000
+ codeword versus the number of hard-decision errors in the received word
- simulated transmissions at 
+ for a run with 1000 simulated transmissions at 
-\begin_inset Formula $SNR=-24$
+\begin_inset Formula $\mathrm{SNR}=-24$
 \end_inset
 
  dB, just slightly above the decoding threshold.
- Note that both mean and variance of the required number of trials increase
+ The timeout parameter was 
- steeply with the number of errors in the received word.
+\begin_inset Formula $T=10^{5}$
- Execution time of the FT algorithm is roughly proportional to the number
+\end_inset
- of required trials.
 
+ for this run.
+ No points are shown for 
+\begin_inset Formula $X\le25$
+\end_inset
+
+ because all such words were successfully decoded by the BM algorithm.
+ Figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:N_vs_X"
+
+\end_inset
+
+ shows that the FT algorithm decoded received words with as many as 
+\begin_inset Formula $X=43$
+\end_inset
+
+ symbol errors.
+ The results also show that, on average, the number of trials increases
+ with the number of errors in the received word.
+ The variability of the decoding time also increases dramatically with the
+ number of errors in the received word.
+ These results also provide insight into the mean and variance of the execution
+ time for the FT algorithm, as execution time will be roughly proportional
+ to the number of required trials.
 \end_layout
 
 \begin_layout Standard
@@ -1356,7 +1492,6 @@ status open
 \begin_inset Graphics
 	filename fig_ntrials_vs_nhard.pdf
 	lyxscale 120
-	scale 120
 
 \end_inset
 
@@ -1377,7 +1512,7 @@ Number of trials needed to decode a received word versus Hamming distance
  between the received word and the decoded codeword, for 1000 simulated
  frames on an AWGN channel with no fading.
  The SNR in 2500 Hz bandwidth is -24 dB (
-\begin_inset Formula $E_{s}/N_{o}=5.7$
+\begin_inset Formula $E_{b}/N_{o}=5.1$
 \end_inset
 
  dB).
@@ -1395,101 +1530,7 @@ Number of trials needed to decode a received word versus Hamming distance
 \end_layout
 
 \begin_layout Subsection
-Comparison with Berlekamp-Massey and Koetter-Vardy
+Simulated results for hinted decoding and Rayleigh fading
-\end_layout
-
-\begin_layout Standard
-Comparisons of decoding performance are usually presented in the professional
- literature as plots of word error rate versus 
-\begin_inset Formula $E_{b}/N_{0}$
-\end_inset
-
-, the signal-to-noise ratio per information bit.
- Results of simulations using the Berlekamp-Massey, Koetter-Vardy, and Franke-Ta
-ylor decoding algorithms on the (63,12) code are presented in this way in
- Figure 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:WER"
-
-\end_inset
-
-.
- For these tests we generated 1000 signals at each signal-to-noise ratio,
- assuming the additive white gaussian noise (AWGN) channel, and processed
- the data using each algorithm.
- As expected, the soft-decision algorithms FT and KV are about 2 dB better
- than the hard-decision BM algorithm.
- FT has a slight edge (about 0.2 dB) over KV with the default settings for
- each algorithm, as implemented in our JT65 decoders.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename fig_wer.pdf
-	lyxscale 120
-	scale 120
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption Standard
-
-\begin_layout Plain Layout
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:WER"
-
-\end_inset
-
-Word error rate (WER) as a function of 
-\begin_inset Formula $E_{b}/N_{0}$
-\end_inset
-
- for non-fading signals in AWGN.
- 
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Because of the importance of error-free transmission in commercial applications,
- plots like that in Figure 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:WER"
-
-\end_inset
-
- often extend downward to much smaller error rates, say
-\begin_inset Formula $10^{-6}$
-\end_inset
-
- or less, .
- The circumstances for minimal amateur-radio QSOs are very different, however.
- Error rates of order 0.1, or ever higher, may be acceptable.
- In this case the essential information is better presented in a plot showing
- the percentage of transmissions copied correctly as a function of signal-to-noi
-se ratio.
- 
 \end_layout
 
 \begin_layout Standard
@@ -1529,7 +1570,6 @@ status open
 \begin_inset Graphics
 	filename fig_psuccess.pdf
 	lyxscale 90
-	scale 90
 
 \end_inset
 
@@ -1665,7 +1705,13 @@ Berlekamp-Massey decoder written by Phil Karn, http://www.ka9q.net/code/fec/
 
 \begin_layout Section
 \start_of_appendix
-Signal to Noise Ratios
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Appendix:SNR"
+
+\end_inset
+
+Appendix: Signal to Noise Ratios
 \end_layout
 
 \begin_layout Standard
@@ -1676,7 +1722,7 @@ The signal to noise ratio in a bandwidth,
 , that is at least as large as the bandwidth occupied by the signal is:
 \begin_inset Formula 
 \begin{equation}
-SNR_{B}=\frac{P_{s}}{N_{o}B}\label{eq:SNR}
+\mathrm{SNR}_{B}=\frac{P_{s}}{N_{o}B}\label{eq:SNR}
 \end{equation}
 
 \end_inset
@@ -1685,18 +1731,18 @@ where
 \begin_inset Formula $P_{s}$
 \end_inset
 
- is the signal power, 
+ is the signal power (W), 
 \begin_inset Formula $N_{o}$
 \end_inset
 
- is one-sided noise power spectral density, and 
+ is one-sided noise power spectral density (W/Hz), and 
 \begin_inset Formula $B$
 \end_inset
 
  is the bandwidth in Hz.
  In amateur radio applications, digital modes are often compared based on
  the SNR defined in a 2.5 kHz reference bandwidth, 
-\begin_inset Formula $SNR_{2.5\,\mathrm{kHz}}$
+\begin_inset Formula $\mathrm{SNR}_{2.5\,\mathrm{kHz}}$
 \end_inset
 
 .
@@ -1717,32 +1763,20 @@ In the professional literature, decoder performance is characterized in
 \begin_inset Formula $N_{o}$
 \end_inset
 
-, or in terms of 
-\begin_inset Formula $E_{s}/N_{o}$
-\end_inset
-
-, the ratio of the energy collected per received symbol, 
-\begin_inset Formula $E_{s}$
-\end_inset
-
-, and 
-\begin_inset Formula $N_{o}$
-\end_inset
-
 .
  Denote the duration of a channel symbol by 
 \begin_inset Formula $\tau_{s}$
 \end_inset
 
  (for JT65, 
-\begin_inset Formula $\tau_{s}=0.375\,\mathrm{s}$
+\begin_inset Formula $\tau_{s}=0.3715\,\mathrm{s}$
 \end_inset
 
 ).
  Signal power is related to the energy per symbol by 
 \begin_inset Formula 
 \begin{equation}
-P_{s}=E_{s}/\tau_{s},\label{eq:signal_power}
+P_{s}=E_{s}/\tau_{s}.\label{eq:signal_power}
 \end{equation}
 
 \end_inset
@@ -1780,36 +1814,28 @@ reference "eq:Eb_Es"
 \end_inset
 
 ), 
-\begin_inset Formula $SNR_{2.5\,\mathrm{kHz}}$
+\begin_inset Formula $\mathrm{SNR}_{2.5\,\mathrm{kHz}}$
 \end_inset
 
  can be written in terms of 
 \begin_inset Formula $E_{b}/N_{o}$
-\end_inset
-
- or 
-\begin_inset Formula $E_{s}/N_{o}$
 \end_inset
 
 :
 \begin_inset Formula 
 \[
-SNR_{2.5\,\mathrm{kHz}}=1.08\times10^{-3}\frac{E_{s}}{N_{o}}=1.23\times10^{-3}\frac{E_{b}}{N_{o}}.
+\mathrm{SNR}_{2.5\,\mathrm{kHz}}=1.23\times10^{-3}\frac{E_{b}}{N_{o}}.
 \]
 
 \end_inset
 
-
-\end_layout
-
-\begin_layout Standard
 If all quantities are expressed in dB, then:
 \end_layout
 
 \begin_layout Standard
 \begin_inset Formula 
 \[
-SNR_{2.5\,\mathrm{kHz}}=(E_{b}/N_{o})_{\mathrm{dB}}-29.66\,\mathrm{dB}=(E_{s}/N_{o})_{\mathrm{dB}}-29.10\,\mathrm{dB}.
+SNR_{2.5\,\mathrm{kHz}}=(E_{b}/N_{o})_{\mathrm{dB}}-29.1\,\mathrm{dB}.
 \]
 
 \end_inset