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Add figures, refine notation.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6230 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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@ -364,7 +364,11 @@ tric probability distribution.
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\begin_inset Formula $X$
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\begin_inset Formula $X$
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\end_inset
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\end_inset
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as the number of incorrect symbols in the received set, and
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as the number of incorrect symbols in the set of
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\begin_inset Formula $N$
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\end_inset
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symbols, and
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\begin_inset Formula $x$
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\begin_inset Formula $x$
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\end_inset
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\end_inset
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@ -400,7 +404,7 @@ tric probability distribution.
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\begin_layout Standard
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\begin_layout Standard
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\begin_inset Formula
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\begin_inset Formula
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\begin{equation}
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\begin{equation}
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P(x|N,X,s)=\frac{\binom{X}{x}\binom{N-X}{s-x}}{\binom{N}{s}}\label{eq:hypergeometric_pdf}
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P(x=\epsilon|N,X,s)=\frac{\binom{X}{x}\binom{N-X}{s-\epsilon}}{\binom{N}{s}}\label{eq:hypergeometric_pdf}
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\end{equation}
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\end{equation}
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\end_inset
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\end_inset
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@ -444,6 +448,35 @@ hygepdf(
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\end_inset
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\end_inset
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.
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.
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The cumulative probability that
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\emph on
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at least
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\emph default
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\begin_inset Formula $\epsilon$
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\end_inset
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errors are captured in a subset of
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\begin_inset Formula $s$
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\end_inset
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erased symbols selected from a group of
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\begin_inset Formula $N$
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\end_inset
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symbols containing
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\begin_inset Formula $X$
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\end_inset
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errors is
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\begin_inset Formula
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\begin{equation}
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P(x\ge\epsilon|N,X,s)=\sum_{j=\epsilon}^{N}P(x=j|N,X,s)\label{eq:cumulative_prob}
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\end{equation}
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\end_inset
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\end_layout
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\end_layout
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\begin_layout Paragraph
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\begin_layout Paragraph
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@ -959,10 +992,50 @@ status open
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\begin_inset Caption Standard
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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\begin_layout Plain Layout
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Percentage of JT65 messages successfully decoded as a function of SNR in
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\begin_inset CommandInset label
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2.5 kHz bandwidth.
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LatexCommand label
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name "fig:Psuccess"
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\end_inset
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Percentage 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.
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Results are shown for the hard-decision Berlekamp-Massey (BM) and soft-decision
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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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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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\end_inset
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,
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\begin_inset Formula $n_{hard}<44$
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\end_inset
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.
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\end_layout
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\end_layout
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\end_inset
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\end_inset
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@ -977,6 +1050,104 @@ Percentage of JT65 messages successfully decoded as a function of SNR in
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\end_inset
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\end_inset
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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_wer.pdf
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lyxscale 120
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scale 120
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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:WER"
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\end_inset
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Word error rate as a function of
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\begin_inset Formula $E_{s}/N_{o}$
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\end_inset
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.
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The results from 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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plotted as the fraction of frames that are not decoded vs symbol SNR.
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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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_ntrials_vs_nhard.pdf
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lyxscale 120
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scale 120
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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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The number of trials needed to decode a received word vs the Hamming distance
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between the received word and the decoded codeword plotted for 1000 simulated
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frames with -24 dB SNR in 2500 Hz bandwidth (
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\begin_inset Formula $E_{s}/N_{o}=5.7$
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\end_inset
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dB).
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Execution time will be roughly proportional to the number of trials.
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The mean and variance of the number of trials (and execution time) increase
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with the number of errors in the received word.
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_layout
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\begin_layout Itemize
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\begin_layout Itemize
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