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Mostly minor editing. I think it's mostly done now, except for Section 7.

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git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6368 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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Joe Taylor 2016-01-09 00:09:12 +00:00
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@ -117,7 +117,7 @@ A major reason for the success and popularity of JT65 is its use of a strong
error-correction code: a short block-length, low-rate Reed-Solomon code
based on a 64-symbol alphabet.
Until now, nearly all programs implementing JT65 have used the patented
Koetter-Vardy (KV) algebraic soft-decision decoder
Kötter-Vardy (KV) algebraic soft-decision decoder
\begin_inset CommandInset citation
LatexCommand cite
key "kv2001"
@ -155,9 +155,8 @@ The JT65 protocol specifies transmissions that normally start one second
into a UTC minute and last for 46.8 seconds.
Receiving software therefore has up to several seconds to decode a message
before the start of the next minute, when the operator sends a reply.
With today's personal computers, this relatively long time available for
decoding a short message encourages experimentation with decoders of high
computational complexity.
With today's personal computers, this relatively long available time encourages
experimentation with decoders of high computational complexity.
As a result, on a typical fading channel the FT algorithm can extend the
decoding threshold by many dB over the hard-decision Berlekamp-Massey decoder,
and by a meaningful amount over the KV decoder.
@ -247,7 +246,7 @@ The minimum Hamming distance of the JT65 code is
\end_inset
, which means that any particular codeword differs from all other codewords
in at least 52 symbol positions.
in at least 52 or the 63 symbol positions.
\end_layout
@ -1326,10 +1325,10 @@ If
\end_inset
and
\begin_inset Formula $X_{1}=X.$
\begin_inset Formula $X_{1}=X,$
\end_inset
and save the codeword.
\end_layout
\begin_layout Enumerate
@ -1375,7 +1374,7 @@ Otherwise, declare decoding failure and exit.
\begin_layout Enumerate
An acceptable codeword has been found.
Declare a successful decode and return this codeword.
Declare a successful decode and return the saved codeword.
\end_layout
\end_inset
@ -1416,7 +1415,7 @@ stochastic erasures-only list decoding algorithm
\begin_inset Quotes erd
\end_inset
, described in reference
described in reference
\begin_inset CommandInset citation
LatexCommand cite
key "ls2009"
@ -1462,14 +1461,14 @@ much
\emph default
smaller list of messages (say, a few thousand messages or less) that we
might suppose would be among the most likely ones to be received.
One such situation exists when making short ham-radio contacts that exchange
minimal information including callsigns, signal reports, perhaps Maidenhead
locators, and acknowledgments.
One such favorable situation exists when making short ham-radio contacts
that exchange minimal information including callsigns, signal reports,
perhaps Maidenhead locators, and acknowledgments.
On the EME path or a VHF or UHF band with limited geographical coverage,
the most common received messages often originate from callsigns that have
been decoded before.
Saving a list of previously decoded callsigns and associated locators makes
it easy to generate lists of hypothetical messages and their corresponding
it easy to generate a list of hypothetical messages and their corresponding
codewords at very little computational expense.
The resulting candidate codewords can be tested in almost the same way
as those generated by the probabilistic method described in Section
@ -1507,7 +1506,12 @@ For hinted decoding we again invoke a ratio threshold test, but in this
case we use it to answer a more limited question.
Over the full list of messages considered likely, we want to know whether
a suitable metric can distinguish with confidence between the one correct
codeword and all others in the generated list.
codeword and all others in the generated list --- or, alternatively, to
determine that the correct codeword is
\emph on
not
\emph default
contained in the list.
We again find that the most effective metric involves a comparison of
\begin_inset Formula $u_{1}$
\end_inset
@ -1521,12 +1525,12 @@ For hinted decoding we again invoke a ratio threshold test, but in this
The criterion for comparison is chosen empirically to maximize the number
of correct decodes while ensuring that false decodes are rare.
Because tested candidate codewords are drawn from a list typically no longer
than a few thousand, rather than
than a few thousand entries, rather than
\begin_inset Formula $2^{72},$
\end_inset
the limit can can be more relaxed than that used in the FT algorithm.
THus, for the limited subset of messages suggested by operator experience
Thus, for the limited subset of messages suggested by previous experience
to be likely, hinted decodes can be obtained at lower signal levels than
required for the full universe of
\begin_inset Formula $2^{72}$
@ -1535,6 +1539,18 @@ For hinted decoding we again invoke a ratio threshold test, but in this
possible messages.
\end_layout
\begin_layout Standard
Pseudo-code for the hinted decode or
\begin_inset Quotes eld
\end_inset
Deep Search
\begin_inset Quotes erd
\end_inset
algorithm is presented in an accompanying text box.
\end_layout
\begin_layout Standard
\begin_inset Float algorithm
wide false
@ -1584,14 +1600,14 @@ If
\end_inset
by setting
\begin_inset Formula $u_{2}=u_{1},$
\begin_inset Formula $u_{2}=u_{1}.$
\end_inset
then set
\begin_inset Formula $u_{1}=u.$
Then set
\begin_inset Formula $u_{1}=u$
\end_inset
and save the codeword.
\end_layout
\begin_layout Enumerate
@ -1611,12 +1627,22 @@ If
\end_layout
\begin_layout Enumerate
Otherwise, declare hinted-decoding failure and exit.
Otherwise, declare decoding failure and exit.
\end_layout
\begin_layout Enumerate
An acceptable hinted decode has been found.
Declare a successful result and return this codeword.
Declare a successful result and return the saved codeword and the value
\begin_inset Formula $q=100*(u_{1}-bu_{2})$
\end_inset
as a confidence indicator.
By default we use
\begin_inset Formula $b=1.12$
\end_inset
.
\end_layout
\end_inset
@ -1667,7 +1693,7 @@ reference "sec:Appendix:SNR"
.
Examples of both types of plot are included in the following discussion,
where we describe simulations carried out to compare performance of FT
with other algorithms and with theoretical expectations.
and hinted decoding with other algorithms and with theoretical expectations.
We have also used simulations to establish suitable default values for
the acceptance parameters
\begin_inset Formula $X_{0},$
@ -1723,11 +1749,11 @@ reference "fig:bodide"
\end_inset
also shows results calculated from theory for comparison with the BM results.
also shows results calculated from theoretical probability distributions
for comparison with the BM results.
The simulated BM results agree with theory to within about 0.1 dB.
This difference between simulated BM results and theory is caused by small
errors in the estimates of time- and frequency-offset of the received signal
in the simulated data.
This differences are caused by small errors in the estimates of time and
frequency offset of the received signal in the simulated data.
Such
\begin_inset Quotes eld
\end_inset
@ -1741,7 +1767,7 @@ sync losses
\end_layout
\begin_layout Standard
As expected, the soft-decision algorithms, FT and KV, are about 2 dB better
As expected, the soft-decision algorithms FT and KV are about 2 dB better
than the hard-decision BM algorithm.
In addition, FT has an edge over KV that increases from
\begin_inset Formula $\sim0.2$
@ -1928,7 +1954,11 @@ name "fig:WER2"
\end_inset
Percent of JT65 messages copied as a function of SNR in 2500 Hz bandwidth.
Percent of JT65 messages copied as a function of
\begin_inset Formula $\mathrm{SNR}{}_{2500},$
\end_inset
assuming additive white gaussian noise and no fading.
Numbers adjacent to curves specify values of timeout parameter
\begin_inset Formula $T$
\end_inset
@ -1976,11 +2006,11 @@ reference "fig:N_vs_X"
the number of hard-decision errors in the received word.
This run used 1000 simulated transmissions at
\begin_inset Formula $\mathrm{SNR}=-24$
\begin_inset Formula $\mathrm{SNR_{2500}}=-24$
\end_inset
dB, just slightly above the decoding threshold, and the timeout parameter
was
dB, just slightly above the decoding threshold, with timeout parameter
\begin_inset Formula $T=10^{5}.$
\end_inset
@ -2004,8 +2034,8 @@ reference "fig:N_vs_X"
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.
The variability of decoding time also increases dramatically with the number
of errors in the received word.
These results provide insight into the mean and variance of the execution
time for the FT algorithm, since execution time is roughly proportional
to the number of required trials.
@ -2044,9 +2074,8 @@ Number of trials needed to decode a received word versus Hamming distance
\end_inset
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
\begin_inset Formula $-24$
transmissions on an AWGN channel with no fading and
\begin_inset Formula $\mathrm{SNR}{}_{2500}=-24$
\end_inset
dB, which corresponds to
@ -2101,18 +2130,21 @@ reference "fig:Psuccess"
\begin_layout Standard
It is interesting to note that while Rayleigh fading severely degrades the
success rate of the BM decoder, the penalties are much smaller with both
FT and hinted decoding.
FT and
\begin_inset Quotes eld
\end_inset
Deep Search
\begin_inset Quotes erd
\end_inset
decoding.
Simulated Doppler spreads of 0.2 Hz actually increased the FT and DS decoding
rates slightly at SNRs close to the decoding threshold, presumably because
with the low-rate JT65 code signal peaks can be enough to produce good
copy.
\end_layout
\begin_layout Standard
(*** New data will be used for the DS curves.
***)
\end_layout
\begin_layout Standard
\begin_inset Float figure
wide false
@ -2140,11 +2172,14 @@ name "fig:Psuccess"
\end_inset
Percentage of JT65 messages successfully decoded as a function of SNR in
2500 Hz bandwidth.
Percentage of JT65 messages successfully decoded as a function of
\begin_inset Formula $\mathrm{SNR}{}_{2500}$
\end_inset
.
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 (
Curves labeled DS correspond to the hinted-decode or
\begin_inset Quotes eld
\end_inset
@ -2152,8 +2187,8 @@ Deep Search
\begin_inset Quotes erd
\end_inset
) algorithm.
Numbers adjacent to the curves are the simulated Doppler spreads in Hz.
algorithm.
Numbers adjacent to the curves are simulated Doppler spreads in Hz.
The curve labeled
\begin_inset Quotes eld
\end_inset
@ -2162,8 +2197,8 @@ Sync
\begin_inset Quotes erd
\end_inset
illustrates the rate of correct time and frequency synchronization in the
decoder presently implemented in program
illustrates the success rate of correct time and frequency synchronization
in the decoder presently implemented in program
\emph on
WSJT-X
\emph default
@ -2247,7 +2282,7 @@ key "kv2001"
\end_inset
“Algebraic soft-decision decoding of Reed-Solomon codes,” R.
Köetter and A.
Kötter and A.
Vardy,
\emph on
IEEE Transactions on Information Theory
@ -2276,6 +2311,22 @@ WSJT Home Page
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "3"
key "lc2004"
\end_inset
\emph on
Error Control Coding, 2nd Edition
\emph default
, Shu Lin and Daniel J.
Costello, Pearson-Prentice Hall, 2004.
\end_layout
\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "4"
key "lhmg2010"
\end_inset
@ -2294,7 +2345,7 @@ IEEE Communications Letters
\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "4"
label "5"
key "lk2008"
\end_inset
@ -2313,25 +2364,7 @@ GLOBECOM
\begin_inset Quotes erd
\end_inset
2008 proceedings
\emph default
.
\end_layout
\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "5"
key "lc2004"
\end_inset
\emph on
Error Control Coding, 2nd Edition
\emph default
, Shu Lin and Daniel J.
Costello, Pearson-Prentice Hall, 2004.
2008 proceedings.
\end_layout
\begin_layout Bibliography