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Reduce gain on 2d cumulative spectrum, to be more consistent with others.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6289 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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Joe Taylor
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@ -125,6 +125,18 @@ 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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@ -427,7 +439,7 @@ 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.
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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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@ -485,7 +497,7 @@ Example 1:
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\end_layout
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\begin_layout Standard
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Suppose a codeword contains
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Suppose a received word contains
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\begin_inset Formula $X=40$
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\end_inset
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@ -556,7 +568,8 @@ How might we best choose the number of symbols to erase, in order to maximize
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symbols.
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Decoding will then be assured if the set of erased symbols contains at
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least 37 errors, and with
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least 37 errors.
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With
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\begin_inset Formula $N=63$
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\end_inset
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@ -689,8 +702,9 @@ 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 identifies the most likely value for each symbol based
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on the largest signal-plus-noise power in 64 frequency bins.
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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 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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@ -848,8 +862,12 @@ 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 is used to limit the algorithm's execution time if no codewords
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within soft distance
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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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\begin_inset Formula $d_{a}$
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\end_inset
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@ -912,7 +930,11 @@ 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 the maximum allowed number, go to 2.
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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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Otherwise, declare decoding failure and exit.
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\end_layout
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@ -933,42 +955,121 @@ best
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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 Comparison with KVASD
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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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Possible figures:
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\end_layout
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\begin_layout Itemize
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histogram of
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\begin_inset Formula $s$
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\end_inset
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(number of erasures) for successful decodes with HF and EME data
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\end_layout
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\begin_layout Itemize
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histogram of
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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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ntrials
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moonbounce
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\begin_inset Quotes erd
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\end_inset
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(or execution time)
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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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\end_layout
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\begin_layout Itemize
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Number of decodes vs.
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ntrials
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\begin_layout Section
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Results and Comparisons
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\end_layout
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\begin_layout Itemize
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Probability of successful decode vs.
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Es/No or S/N in 2500 Hz BW
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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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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:Psuccess"
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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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@ -981,8 +1082,8 @@ status open
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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 120
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scale 120
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lyxscale 150
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scale 150
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\end_inset
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@ -999,7 +1100,7 @@ name "fig:Psuccess"
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\end_inset
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Percentage of JT65 messages (
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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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@ -1007,38 +1108,36 @@ 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.
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These results are for the idealized situation of a non-fading signal in
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additive white Gaussian noise (AWGN).
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Results are shown for the hard-decision Berlekamp-Massey (BM) and soft-decision
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Franke-Taylor (FT) decoding algorithms.
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Results for the FT algorithm are shown for two different sets of time-out
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and acceptance criteria.
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FT-1 was obtained with a limit of
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\begin_inset Formula $10^{4}$
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\end_inset
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erasure vectors and with acceptance criteria
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\begin_inset Formula $d_{a}<72$
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\end_inset
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and
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\begin_inset Formula $n_{hard}<42$
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\end_inset
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, and FT-2 corresponds to
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\begin_inset Formula $10^{5}$
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\end_inset
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erasure vectors and
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\begin_inset Formula $d_{a}<76$
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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 $n_{hard}<44$
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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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\end_layout
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\end_inset
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@ -147,10 +147,10 @@ subroutine jt65a(dd0,npts,newdat,nutc,nf1,nf2,nfqso,ntol,nsubmode, &
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1012 format(i4.4,i4,i5,f6.1,f8.0,i4,3x,a22,' JT65',i4)
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call flush(6)
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call flush(13)
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! write(79,3001) nutc,nint(sync1),nsnr,dtx-1.0,nfreq,ncandidates, &
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! nhard_min,ntotal_min,ntry,naggressive,nft,nqual,decoded
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!3001 format(i4.4,i3,i4,f6.2,i5,i7,i3,i4,i8,i3,i2,i5,1x,a22)
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! flush(79)
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write(79,3001) nutc,nint(sync1),nsnr,dtx-1.0,nfreq,ncandidates, &
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nhard_min,ntotal_min,ntry,naggressive,nft,nqual,decoded
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3001 format(i4.4,i3,i4,f6.2,i5,i7,i3,i4,i8,i3,i2,i5,1x,a22)
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flush(79)
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endif
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decoded0=decoded
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freq0=freq
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@ -161,7 +161,7 @@ void CPlotter::draw(float swide[], bool bScroll) //dr
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}
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m_sum[i]=sum;
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}
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if(m_bCumulative) y2=2.5*gain2d*(m_sum[i]/m_binsPerPixel + m_plot2dZero);
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if(m_bCumulative) y2=gain2d*(m_sum[i]/m_binsPerPixel + m_plot2dZero);
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if(m_Flatten==0) y2 += 15; //### could do better! ###
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if(m_bLinearAvg) { //Linear Avg (yellow)
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