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131
lib/ftrsd/ftrsd_paper/ftrsd.lyx
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@ -84,15 +84,6 @@ Steven J.
Taylor, K1JT
\end_layout
\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents
\end_inset
\end_layout
\begin_layout Section
\begin_inset CommandInset label
LatexCommand label
@ -117,8 +108,8 @@ moonbounce
\end_inset
) communication, where the scattered return signals are always weak.
It was soon found that JT65 also facilitates worldwide communication on
the HF bands with low power, modest antennas, and efficient spectral usage.
It was soon found that JT65 also enables worldwide communication on the
HF bands with low power, modest antennas, and efficient spectral usage.
\end_layout
\begin_layout Standard
@ -133,7 +124,7 @@ key "kv2001"
\end_inset
, licensed to and implemented by K1JT in a closed-source executable for
, licensed to and implemented by K1JT as a closed-source executable for
use only in amateur radio applications.
Since 2001 the KV decoder has been considered the best available soft-decision
decoder for Reed Solomon codes.
@ -1121,7 +1112,7 @@ reference "sec:Theory,-Simulation,-and"
\end_inset
, we use simulations to set an empirical acceptance threshold
\begin_inset Formula $r_{0}$
\begin_inset Formula $r_{1}$
\end_inset
that maximizes the probability of correct decodes while ensuring a low
@ -1145,7 +1136,7 @@ Technically the FT algorithm is a list decoder.
\begin_inset Formula $d_{s}$
\end_inset
are less than conservatively specified limits
are less than specified limits
\begin_inset Formula $X_{0}$
\end_inset
@ -1162,7 +1153,7 @@ Technically the FT algorithm is a list decoder.
\begin_inset Formula $r<r_{1}$
\end_inset
are used to validate additional decodes that did not pass the first test.
are used to validate additional codewords that did not pass the first test.
A timeout is used to limit the algorithm's execution time if no acceptable
codeword is found in a reasonable number of trials,
\begin_inset Formula $T$
@ -1390,17 +1381,17 @@ The FT algorithm is completely general: with equal sensitivity it recovers
\emph on
much
\emph default
smaller list of messages (say, a few thousand messages or less) that may
be among the most likely ones to be received.
smaller list of messages (say, a few thousand messages or less) that we
can guess may 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.
On the EME path or on a VHF or UHF band with limited geographical coverage,
the most likely received messages often originate from callsigns that have
been decoded before.
Saving a list of previously decoded callsigns makes it easy to generate
lists of hypothetical messages and their corresponding codewords, at very
little computational expense.
Saving a list of previously decoded callsigns and associated locators makes
it easy to generate lists of hypothetical messages and their corresponding
codewords at very little computational expense.
The resulting candidate codewords can be tested in the same way as those
generated by the probabilistic method described in Setcion
\begin_inset CommandInset ref
@ -1454,16 +1445,8 @@ For hinted decoding we again invoke a ratio threshold test, but in this
\begin_inset Formula $r_{2},$
\end_inset
for what is
\begin_inset Quotes eld
\end_inset
small enough
\begin_inset Quotes erd
\end_inset
to establish adequate confidence, while still ensuring that false decodes
are rare.
that is small enough to establish adequate confidence, while still ensuring
that false decodes are rare.
Because tested candidate codewords are drawn from a list typically no longer
than a few thousand, rather than
\begin_inset Formula $2^{72},$
@ -1473,22 +1456,14 @@ small enough
\begin_inset Formula $r_{2}$
\end_inset
can set a more relaxed limit than
\begin_inset Formula $r_{1},$
can be a more relaxed limit than the
\begin_inset Formula $r_{1}$
\end_inset
as used in the FT algorithm.
For the limited subset of messages established by operator experience as
\begin_inset Quotes eld
\end_inset
likely,
\begin_inset Quotes erd
\end_inset
hinted decodes can be obtained at lower signal levels than required for
decodes obtained from the full universe of
used in the FT algorithm.
For the limited subset of messages that operator experience suggests to
be likely, hinted decodes can be obtained at lower signal levels than required
for those obtained from the full universe of
\begin_inset Formula $2^{72}$
\end_inset
@ -1512,11 +1487,7 @@ Comparisons of decoding performance are usually presented in the professional
\end_inset
, the ratio of the energy collected per information bit to the one-sided
noise power spectral density,
\begin_inset Formula $N_{0}$
\end_inset
.
noise power spectral density.
For weak-signal amateur radio work, performance is more conveniently presented
as the probability of successfully decoding a received word plotted against
signal-to-noise ratio in a 2500 Hz reference bandwidth,
@ -1540,12 +1511,12 @@ reference "sec:Appendix:SNR"
\end_inset
.
Examples of both types of plot are included in the following discussion,
where we describe a number of simulations carried out to compare performance
of the FT algorithm with others, and with theoretical expectations.
Examples of both presentations are included in the following discussion,
where we describe simulations carried out to compare performance of FT
with other algorithms, and with theoretical expectations.
We have also used simulations to establish suitable default values for
the acceptance parameters
\begin_inset Formula $h_{0},$
\begin_inset Formula $X_{0},$
\end_inset
@ -1556,8 +1527,12 @@ reference "sec:Appendix:SNR"
\begin_inset Formula $d_{1},$
\end_inset
\begin_inset Formula $r_{1},$
\end_inset
and
\begin_inset Formula $r_{1}.$
\begin_inset Formula $r_{2}.$
\end_inset
@ -1582,8 +1557,8 @@ reference "fig:bodide"
.
For these tests we generated at least 1000 signals at each signal-to-noise
ratio, assuming the additive white gaussian noise (AWGN) channel, and processed
the data using each algorithm.
ratio, assuming the additive white gaussian noise (AWGN) channel, and we
processed 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 measurements statistically meaningful.
@ -1594,11 +1569,11 @@ reference "fig:bodide"
\end_inset
also shows theoretical results for comparison with the BM results.
also shows results calculated from theory 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 results.
in the simulated data.
Such
\begin_inset Quotes eld
\end_inset
@ -1615,7 +1590,7 @@ sync losses
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.
On the other hand, the execution time for FT with
On the other hand, the execution time for FT with timeout parameter
\begin_inset Formula $T=10^{5}$
\end_inset
@ -1624,7 +1599,7 @@ As expected, the soft-decision algorithms, FT and KV, are about 2 dB better
\begin_inset Formula $T=10^{5}$
\end_inset
is small enough to be practical on most computers.
is small enough to be practical on most of today's home computers.
\end_layout
@ -1694,7 +1669,7 @@ reference "fig:bodide"
\end_inset
often extend downward to much smaller error rates, say
often extend downward to even smaller error rates, say
\begin_inset Formula $10^{-6}$
\end_inset
@ -1711,18 +1686,18 @@ reference "fig:WER2"
\end_inset
shows the FT results for
shows in this format the FT results for
\begin_inset Formula $T=10^{5}$
\end_inset
and the KV results that were shown in Figure
and the KV results from Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:bodide"
\end_inset
in this format along with additional FT results for
, along with additional FT results for
\begin_inset Formula $T=10^{4},\:10^{3},\:10^{2}$
\end_inset
@ -1731,14 +1706,13 @@ reference "fig:bodide"
\end_inset
.
The KV results are plotted with open squares.
It is apparent that the FT decoder produces more decodes than KV when
\begin_inset Formula $T=10^{4}$
\end_inset
or larger.
It also provides a very significant gain over the hard-decision BM decoder
even when limited to at most 10 trials.
even when limited to 10 or fewer trials.
\end_layout
\begin_layout Standard
@ -1794,12 +1768,12 @@ Percent of JT65 messages copied as a function of SNR in 2500 Hz bandwidth.
\end_layout
\begin_layout Standard
The timeout parameter
Timeout parameter
\begin_inset Formula $T$
\end_inset
employed in the FT algorithm is the maximum number of symbol-erasure trials
allowed for a particular attempt at decoding a received word.
is the maximum number of symbol-erasure trials allowed for a particular
attempt at decoding a received word.
Most successful decodes take only a small fraction of the maximum allowed
number of trials.
Figure
@ -1810,8 +1784,9 @@ reference "fig:N_vs_X"
\end_inset
shows the number of stochastic erasure trials required to find the correct
codeword versus the number of hard-decision errors in the received word
for a run with 1000 simulated transmissions at
codeword vs.
the number of hard-decision errors in the received word, for a run with
1000 simulated transmissions at
\begin_inset Formula $\mathrm{SNR}=-24$
\end_inset
@ -1843,7 +1818,7 @@ reference "fig:N_vs_X"
The variability of the 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 will be roughly proportional
time for the FT algorithm, since execution time is roughly proportional
to the number of required trials.
\end_layout
@ -1928,11 +1903,15 @@ reference "fig:Psuccess"
We include three curves for each decoding algorithm: one for the AWGN channel
and no fading, and two more for simulated Doppler spreads of 0.2 and 1.0
Hz.
The simulated Doppler spreads are comparable to those encountered on HF
ionospheric paths and for EME at VHF and lower UHF bands.
These simulated Doppler spreads are comparable to those encountered on
HF ionospheric paths and also for EME at VHF and the lower UHF bands.
For reference, we note that the JT65 symbol rate is about 2.69 Hz.
(*** A little more description of hinted decoding is needed here, and new
data for the DS curves.***)
\end_layout
\begin_layout Standard
(*** A little more description is needed here, along with new data for the
DS curves.***)
\end_layout
\begin_layout Standard