mirror of https://github.com/saitohirga/WSJT-X.git
New versions of two figures, and some text additions. (More to come!)
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6301 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor
parent
4f8d3dffc7
commit
ef49f6dbd6
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@ -2,22 +2,24 @@
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# run: gnuplot fig_psuccess.gnuplot
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# then: pdflatex fig_psuccess.tex
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#
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set term epslatex standalone size 20cm,10cm
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set term epslatex standalone size 6in,4in
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set output "fig_psuccess.tex"
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set xlabel "SNR in 2500 Hz BW (dB)"
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set xlabel "SNR in 2500 Hz Bandwidth (dB)"
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set ylabel "Percent copy"
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set style func linespoints
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set key on top outside nobox
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set key off
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set tics in
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set mxtics 2
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set mytics 2
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set grid
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plot "ftdata-10000.dat" using 1:2 every ::1 with linespoints pt 4 title 'FT-10K', \
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"ftdata-100000.dat" using 1:2 every ::1 with linespoints pt 5 title 'FT-100K', \
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"ftdata-1000-rf.dat" using 1:2 every ::1 with linespoints pt 7 title 'FT-1K-RF', \
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"ftdata-100-rf.dat" using 1:2 every ::1 with linespoints pt 8 title 'FT-100-RF', \
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"bmdata.dat" using 1:2 with linespoints pt 9 title 'BM', \
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"bmdata-rf.dat" using 1:2 with linespoints pt 10 title 'BM-RF', \
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"kvasd-7999-rf.dat" using 1:2 every ::1 with linespoints pt 12 title 'KV-8-RF', \
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"kvasd-11999.dat" using 1:2 every ::1 with linespoints pt 13 title 'KV-12', \
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"kvasd-11999-rf.dat" using 1:2 every ::1 with linespoints pt 14 title 'KV-12-RF'
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plot [-30:-18] [0:105] "stats_0.0" using 1:($3)/10.0 with linespoints lt 4 pt 1 title 'Sync', \
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"stats_0.0" using 1:($4)/10.0 with linespoints lt 2 lw 2 pt 2 title 'BB 0', \
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"stats_0.0" using 1:($5)/10.0 with linespoints lt 1 lw 2 pt 3 title 'FT 0', \
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"stats_0.0" using 1:($6)/10.0 with linespoints lt 3 lw 2 pt 4 title 'DS 0', \
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"stats_0.2" using 1:($4)/10.0 with linespoints lt 2 pt 2 title 'BB 0.2', \
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"stats_0.2" using 1:($5)/10.0 with linespoints lt 1 pt 3 title 'FT 0.2', \
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"stats_0.2" using 1:($6)/10.0 with linespoints lt 3 pt 4 title 'DS 0.2', \
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"stats_1.0" using 1:($4)/10.0 with linespoints lt 2 pt 2 title 'BB 1', \
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"stats_1.0" using 1:($5)/10.0 with linespoints lt 1 pt 3 title 'FT 1', \
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"stats_1.0" using 1:($6)/10.0 with linespoints lt 3 pt 4 title 'DS 1', \
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"psuccess.lab" with labels
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Binary file not shown.
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@ -2,18 +2,18 @@
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# run: gnuplot fig_wer.gnuplot
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# then: pdflatex fig_wer.tex
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#
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set term epslatex standalone size 12cm,8cm
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set term epslatex standalone size 6in,4in
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set output "fig_wer.tex"
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set xlabel "$E_s/N_o$ (dB)"
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set ylabel "WER"
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set xlabel "$E_b/N_0$ (dB)"
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set ylabel "Word Error Rate"
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set style func linespoints
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set key on top outside nobox
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set key off
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set tics in
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set mxtics 2
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set mytics 10
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set grid
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set logscale y
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plot "ftdata-10000.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 5 title 'FT-10K', \
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"ftdata-100000.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 7 title 'FT-100K', \
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"kvasd-11999.dat" using ($1+29.7):(1-$2) every ::1 with linespoints pt 8 title 'KV-11.999', \
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"bmdata.dat" using ($1+29.7):(1-$2) with linespoints pt 7 title 'BM'
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plot [3:9] "ftdata-100000.dat" using ($1+29.1):(1-$2) with linespoints pt 7 title 'FT-100K', \
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"kvasd-11999.dat" using ($1+29.1):(1-$2) with linespoints pt 8 title 'KV-11.999', \
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"bmdata.dat" using ($1+29.1):(1-$2) with linespoints pt 7 title 'BM', \
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"wer.lab" with labels
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Binary file not shown.
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@ -86,21 +86,20 @@ Steven J.
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\end_layout
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\begin_layout Abstract
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The JT65 mode has revolutionized amateur-radio weak-signal communication
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The JT65 protocol has revolutionized amateur-radio weak-signal communication
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by enabling amateur radio operators with small antennas and relatively
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low-power transmitters to communicate over propagation paths not usable
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with traditional technologies.
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A major reason for the success and popularity of JT65 is its use of a strong
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error-correction code: a short block-length, low-rate Reed-Solomon code
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based on a 64-symbol alphabet.
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Since 2004, most JT65 decoders have used the patented Koetter-Vardy (KV)
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algebraic soft-decision decoder, licensed to K1JT and implemented in a
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closed-source program for use in amateur radio applications.
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Since 2004, most programs implementing JT65 have used the patented Koetter-Vard
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y (KV) algebraic soft-decision decoder, licensed to K1JT and implemented
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in a closed-source program for use in amateur radio applications.
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We describe here a new open-source alternative called the Franke-Taylor
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(FT, or K9AN-K1JT) algorithm.
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It is conceptually simple, built around the well-known Berlekamp-Massey
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errors-and-erasures algorithm, and performs at least as well as the KV
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decoder.
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errors-and-erasures algorithm, and performs even better than the KV decoder.
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\end_layout
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\begin_layout Section
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@ -125,18 +124,6 @@ on with a Reed-Solomon code.
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\begin_inset Formula $(n,k)$
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\end_inset
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, and the
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\begin_inset Quotes eld
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\end_inset
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rate
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\begin_inset Quotes erd
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\end_inset
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of the code is
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\begin_inset Formula $k/n$
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\end_inset
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.
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JT65 uses a (63,12) Reed-Solomon code with 64 possible values for each
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symbol.
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@ -146,7 +133,7 @@ rate
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message bits.
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The source-encoded messages conveyed by a 63-symbol JT65 frame thus consist
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of 72 bits.
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of 72 information bits.
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The JT65 code is systematic, which means that the 12 message symbols are
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embedded in the codeword without modification and another 51 parity symbols
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derived from the message symbols are added to form a codeword of 63 symbols.
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@ -439,7 +426,7 @@ nchoosek(
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\begin_inset Quotes erd
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\end_inset
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in the interpreted language GNU Octave, as well as many free online calculators.
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in the interpreted language GNU Octave, as well as many free online calculators
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The hypergeometric probability mass function defined in Eq.
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(
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\begin_inset CommandInset ref
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@ -702,9 +689,9 @@ Example 3 shows how reliable information about symbol quality should make
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\begin_layout Standard
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The FT algorithm uses two quality indices made available by a noncoherent
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64-FSK demodulator.
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The demodulator The demodulator computes the power spectrum for each symbol
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and identifies the most likely symbol value based on the largest signal-plus-no
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ise power in 64 frequency bins.
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The demodulator computes the power spectrum for each symbol and identifies
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the most likely symbol value based on the largest signal-plus-noise power
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in 64 frequency bins.
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The fractions of total power in the two bins containing the largest and
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second-largest powers (denoted by
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\begin_inset Formula $p_{1}$
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@ -862,12 +849,8 @@ Technically the FT algorithm is a list decoder, potentially generating a
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\end_inset
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.
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A timeout criterion
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\begin_inset Formula $T$
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\end_inset
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is used to limit the algorithm's execution time if no codewords within
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soft distance
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A timeout is used to limit the algorithm's execution time if no codewords
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within soft distance
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\begin_inset Formula $d_{a}$
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\end_inset
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@ -930,11 +913,7 @@ If
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\end_layout
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\begin_layout Enumerate
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If the number of trials is less than
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\begin_inset Formula $T$
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\end_inset
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, the maximum allowed number, go to 2.
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If the number of trials is less than the maximum allowed number, go to 2.
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Otherwise, declare decoding failure and exit.
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\end_layout
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@ -952,206 +931,36 @@ best
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\end_inset
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has been found.
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Declare a successful decode and return this codeword.
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\end_layout
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\begin_layout Paragraph
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Experience-Based Lists of Candidate Codewords
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\end_layout
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\begin_layout Standard
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JT65 was designed and developed to facilitate amateur communication via
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the Moon as a passive reflector.
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Signals propagating over the Earth-Moon-Earth (EME, or
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\begin_inset Quotes eld
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\end_inset
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moonbounce
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\begin_inset Quotes erd
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\end_inset
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) path suffer attenuation of order 240 dB or more, so received signals are
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always weak.
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To be EME-capable an amateur station must have a very sensitive receiver,
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reasonably high power, and a reasonably large antenna on a VHF, UHF, or
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microwave band.
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At a given time the number of stations engaging in this specialized activity
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is probably
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\begin_inset Formula $M<1000$
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\end_inset
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, world-wide.
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EME communications often consist of little more than an exchange of callsigns,
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signal reports, and acknowledgments, so most messages being exchanged are
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likely to appear in a list no more than a few times
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\begin_inset Formula $M^{2}$
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\end_inset
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in length.
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Such lists (and subsets thereof) offer potential alternatives to the stochastic
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method described above for selecting candidate codewords.
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A list of active callsigns can be built up cumulatively from previously
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decoded messages.
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Candidate codewords derived from the list can be injected into the FT algorithm
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at step 5, where the soft distance between the set of received symbols
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and the codeword is computed.
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A decoder taking advantage of this experience-based approach will have
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significant speed and performance advantages over a purely probabilistic
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algorithm.
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However, it must accept the limitation that these advantages apply only
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to messages appearing in the candidate list.
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In the open-source program
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\shape italic
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WSJT-X
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\shape default
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we generate candidate message lists of several different lengths.
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List lengths range from a few times
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\family roman
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\series medium
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\shape up
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\size normal
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\emph off
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\bar no
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\strikeout off
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\uuline off
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\uwave off
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\noun off
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\color none
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\begin_inset Formula $M$
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\end_inset
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up to about
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\begin_inset Formula $M^{2}$
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\end_inset
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.
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Declare a successful decode and return this codeword .
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\end_layout
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\begin_layout Section
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Results and Comparisons
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Comparison with Berlekamp-Massey and Koetter-Vardy
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\end_layout
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\begin_layout Standard
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We measured performance of the Franke-Taylor soft-decision decoder using
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simulations with many thousands of signal realizations at a range of calibrated
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signal-to-noise ratios (SNRs).
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Our first series of tests assumed an ideal additive white Gaussian noise
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(AWGN) channel.
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The dotted curve in Figure
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Comparisons of decoding performance are usually presented in the professional
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literature as plots of word error rate as a function of
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\begin_inset Formula $E_{b}/N_{0}$
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\end_inset
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, the signal-to-noise ratio per information bit.
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Results for the Berlekamp-Massey, Koetter-Vardy, and Franke-Taylor decoding
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algorithms on the (63,12) code are shown in Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:Psuccess"
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reference "fig:WER"
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\end_inset
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shows the fraction of raw symbols expected to be received incorrectly over
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such a channel.
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Filled circles and the short-dashed curve illustrate performance of the
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hard-decision Berlekamp-Massey algorithm, while filled squares and a solid
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curve give results for the FT algorithm with conservative settings for
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the timeout parameter
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\begin_inset Formula $T$
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\end_inset
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and maximum acceptable soft distance
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\begin_inset Formula $d_{a}$
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\end_inset
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.
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Note that sensitivity with soft-decision decoding is about 2 dB better
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than with hard decisions.
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For comparison, open squares and a long-dashed curve show somewhat looser
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settings for timeout and soft distance parameters can gain roughly another
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0.4 dB.
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At this setting the rate of false decodes is no doubt slightly higher,
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though in our simulations it was still found to be
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\begin_inset Formula $<10^{-4}$
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Graphics
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filename fig_psuccess.pdf
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lyxscale 150
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scale 150
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:Psuccess"
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\end_inset
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Fraction of JT65 messages (
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\begin_inset Quotes eld
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\end_inset
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words
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\begin_inset Quotes erd
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\end_inset
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) successfully decoded as a function of SNR in 2.5 kHz bandwidth, for a non-fadin
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g signal in additive white Gaussian noise (AWGN).
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BM: hard-decision Berlekamp-Massey decoder; FT-1: soft-decision Franke-Taylor
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decoder with
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\begin_inset Formula $T=10^{4}$
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\end_inset
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,
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\begin_inset Formula $d_{a}=72$
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\end_inset
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,
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\begin_inset Formula $h_{max}=42$
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\end_inset
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; FT-2: soft-decision decoder with
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\begin_inset Formula $T=10^{5}$
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\end_inset
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,
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\begin_inset Formula $d_{a}=76$
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\end_inset
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,
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\begin_inset Formula $h_{max}=44$
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\end_inset
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.
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algorithms.
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For these initial tests we generated 1000 signals at each signal-to-noise
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ratio, assuming the additive white gaussian noise (AWGN) channel, and processed
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the data using each algorithm.
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It's easy to see that, as expected, the soft-decision algorithms FT and
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KV are about 2 dB better than the hard-decision BM algorithm, and that
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FT has a slight edge (about 0.2 dB) over KV.
|
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|
||||
\end_layout
|
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|
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\end_inset
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|
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||||
\end_layout
|
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|
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\begin_layout Plain Layout
|
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|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
|
@ -1183,19 +992,11 @@ name "fig:WER"
|
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\end_inset
|
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|
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Word error rate (WER) as a function of
|
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\begin_inset Formula $E_{s}/N_{o}$
|
||||
\begin_inset Formula $E_{b}/N_{0}$
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\end_inset
|
||||
|
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for non-fading signals in AWGN.
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||||
This is the same data that is shown in Figure
|
||||
\begin_inset CommandInset ref
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LatexCommand ref
|
||||
reference "fig:Psuccess"
|
||||
|
||||
\end_inset
|
||||
|
||||
, but plotted as the fraction of frames that were not decoded vs symbol
|
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SNR.
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|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
|
@ -1208,11 +1009,116 @@ reference "fig:Psuccess"
|
|||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
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In the professional literature plots like Figure
|
||||
\begin_inset CommandInset ref
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LatexCommand ref
|
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reference "fig:WER"
|
||||
|
||||
\end_inset
|
||||
|
||||
usually extend downward to even smaller error rates, say
|
||||
\begin_inset Formula $10^{-6}$
|
||||
\end_inset
|
||||
|
||||
or less, because of the importance of error-free transmission.
|
||||
The circumstances for minimal amateur-radio QSOs are very different, however:
|
||||
error rates on the order of 0.1, or ever higher, may be acceptable.
|
||||
In this case the essential information is better presented in a plot like
|
||||
Figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:Psuccess"
|
||||
|
||||
\end_inset
|
||||
|
||||
, which shows the percentage of transmissions copied correctly as a function
|
||||
of signal-to-noise ratio in a standard bandwidth.
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
In Figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:Psuccess"
|
||||
|
||||
\end_inset
|
||||
|
||||
we have plotted the results of simulations for signal-to-noise ratios
|
||||
\begin_inset Formula $-30\leq SNR\leq-18$
|
||||
\end_inset
|
||||
|
||||
dB, again using 1000 simulated signals for each point.
|
||||
For each decoding algorithm we include three curves: one for the AWGN channel
|
||||
and no fading, and two more for Doppler spreads of 0.2 and 1.0 Hz.
|
||||
(Note that the JT65 symbol rate is about 2.69 Hz; the simulated Doppler
|
||||
spreads are comparable to those encountered on HF ionospheric paths and
|
||||
for EME at VHF and lower UHF bands.)
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status collapsed
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\align center
|
||||
\begin_inset Graphics
|
||||
filename fig_psuccess.pdf
|
||||
lyxscale 90
|
||||
scale 90
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset Caption Standard
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "fig:Psuccess"
|
||||
|
||||
\end_inset
|
||||
|
||||
Percentage of JT65 messages successfully decoded as a function of SNR in
|
||||
2500 Hz bandwidth.
|
||||
Results are shown for the hard-decision Berlekamp-Massey (BM) and soft-decision
|
||||
Franke-Taylor (FT) decoding algorithms.
|
||||
Curves labeled DS correspond to the hinted-decode (
|
||||
\begin_inset Quotes eld
|
||||
\end_inset
|
||||
|
||||
Deep Search
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
) matched-filter algorithm.
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
\begin_inset Float figure
|
||||
wide false
|
||||
sideways false
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
\align center
|
||||
|
|
@ -1297,6 +1203,40 @@ Word error rate (WER) as a function of
|
|||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
Possible figures:
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
histogram of
|
||||
\begin_inset Formula $s$
|
||||
\end_inset
|
||||
|
||||
(number of erasures) for successful decodes with HF and EME data
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
histogram of
|
||||
\begin_inset Quotes eld
|
||||
\end_inset
|
||||
|
||||
ntrials
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
(or execution time)
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
Number of decodes vs.
|
||||
ntrials
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
Probability of successful decode vs.
|
||||
Es/No or S/N in 2500 Hz BW
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
other...
|
||||
?
|
||||
|
|
|
|||
|
|
@ -0,0 +1,27 @@
|
|||
SNR Files Sync BM FT Hint Total False BadSync
|
||||
--------------------------------------------------------
|
||||
-18.0 1000 1000 1000 1000 1000 1000 0 0
|
||||
-18.5 1000 1000 1000 1000 1000 1000 0 0
|
||||
-19.0 1000 1000 1000 1000 1000 1000 0 0
|
||||
-19.5 1000 1000 1000 1000 1000 1000 0 0
|
||||
-20.0 1000 1000 1000 1000 1000 1000 0 0
|
||||
-20.5 1000 1000 1000 1000 1000 1000 0 0
|
||||
-21.0 1000 1000 1000 1000 1000 1000 0 0
|
||||
-21.5 1000 1000 991 1000 1000 1000 0 0
|
||||
-22.0 1000 1000 918 1000 1000 1000 0 0
|
||||
-22.5 1000 1000 631 1000 1000 1000 0 0
|
||||
-23.0 1000 1000 261 1000 1000 1000 0 0
|
||||
-23.5 1000 1000 57 990 1000 1000 0 0
|
||||
-24.0 1000 1000 0 925 1000 1000 0 0
|
||||
-24.5 1000 1000 0 737 999 999 1 0
|
||||
-25.0 1000 999 0 445 989 989 10 1
|
||||
-25.5 1000 996 0 191 988 988 8 4
|
||||
-26.0 1000 980 0 68 975 975 7 20
|
||||
-26.5 1000 953 0 18 945 945 7 47
|
||||
-27.0 1000 904 0 3 890 890 8 96
|
||||
-27.5 1000 816 0 2 771 771 8 184
|
||||
-28.0 1000 722 0 0 625 625 4 278
|
||||
-28.5 1000 590 0 0 432 432 8 410
|
||||
-29.0 1000 451 0 0 268 268 8 549
|
||||
-29.5 1000 355 0 0 146 146 8 645
|
||||
-30.0 1000 277 0 0 86 86 6 723
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
SNR Files Sync BM FT Hint Total False BadSync
|
||||
--------------------------------------------------------
|
||||
-18.0 1000 998 973 998 998 998 0 2
|
||||
-18.5 1000 1000 960 1000 1000 1000 0 0
|
||||
-19.0 1000 1000 917 1000 1000 1000 0 0
|
||||
-19.5 1000 1000 849 1000 1000 1000 0 0
|
||||
-20.0 1000 1000 725 1000 1000 1000 0 0
|
||||
-20.5 1000 1000 549 1000 1000 1000 0 0
|
||||
-21.0 1000 1000 373 1000 1000 1000 0 0
|
||||
-21.5 1000 1000 216 1000 1000 1000 0 0
|
||||
-22.0 1000 1000 100 998 1000 1000 0 0
|
||||
-22.5 1000 1000 32 998 1000 1000 0 0
|
||||
-23.0 1000 1000 12 991 1000 1000 0 0
|
||||
-23.5 1000 998 2 958 996 996 2 2
|
||||
-24.0 1000 992 0 878 991 991 1 8
|
||||
-24.5 1000 986 0 739 981 981 5 14
|
||||
-25.0 1000 977 0 533 963 963 14 23
|
||||
-25.5 1000 959 0 324 948 948 14 41
|
||||
-26.0 1000 930 0 153 921 921 16 70
|
||||
-26.5 1000 874 0 51 874 874 12 126
|
||||
-27.0 1000 808 0 14 803 803 12 192
|
||||
-27.5 1000 716 0 3 688 688 11 284
|
||||
-28.0 1000 610 0 1 568 568 9 390
|
||||
-28.5 1000 497 0 0 418 418 12 503
|
||||
-29.0 1000 399 0 0 293 293 6 601
|
||||
-29.5 1000 300 0 0 171 171 6 700
|
||||
-30.0 1000 243 0 0 103 103 8 757
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
SNR Files Sync BM FT Hint Total False BadSync
|
||||
--------------------------------------------------------
|
||||
-18.0 1000 998 917 998 998 998 1 2
|
||||
-18.5 1000 998 824 998 998 998 0 2
|
||||
-19.0 1000 999 695 999 999 999 0 1
|
||||
-19.5 1000 999 504 999 999 999 0 1
|
||||
-20.0 1000 1000 300 1000 1000 1000 0 0
|
||||
-20.5 1000 1000 148 1000 1000 1000 0 0
|
||||
-21.0 1000 1000 56 1000 1000 1000 0 0
|
||||
-21.5 1000 1000 10 1000 1000 1000 0 0
|
||||
-22.0 1000 999 3 995 999 999 0 1
|
||||
-22.5 1000 998 0 972 998 998 0 2
|
||||
-23.0 1000 997 0 899 993 993 4 3
|
||||
-23.5 1000 996 0 758 990 990 6 4
|
||||
-24.0 1000 990 0 545 980 980 10 10
|
||||
-24.5 1000 981 0 305 969 969 12 19
|
||||
-25.0 1000 964 0 128 949 949 17 36
|
||||
-25.5 1000 930 0 43 916 916 19 70
|
||||
-26.0 1000 870 0 15 850 850 14 130
|
||||
-26.5 1000 810 0 4 780 780 11 190
|
||||
-27.0 1000 737 0 0 673 673 13 263
|
||||
-27.5 1000 632 0 0 531 531 7 368
|
||||
-28.0 1000 522 0 0 366 366 11 478
|
||||
-28.5 1000 426 0 0 243 243 15 574
|
||||
-29.0 1000 332 0 0 150 150 9 668
|
||||
-29.5 1000 260 0 0 64 64 10 740
|
||||
-30.0 1000 209 0 0 35 35 10 791
|
||||
Loading…
Reference in New Issue