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More polishing of text, fixed typo's, etc.
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Joe Taylor
parent
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@ -84,15 +84,6 @@ Steven J.
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Taylor, K1JT
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset toc
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LatexCommand tableofcontents
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\end_inset
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\end_layout
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\begin_layout Section
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\begin_inset CommandInset label
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LatexCommand label
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@ -117,8 +108,8 @@ moonbounce
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\end_inset
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) communication, where the scattered return signals are always weak.
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It was soon found that JT65 also facilitates worldwide communication on
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the HF bands with low power, modest antennas, and efficient spectral usage.
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It was soon found that JT65 also enables worldwide communication on the
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HF bands with low power, modest antennas, and efficient spectral usage.
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\end_layout
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\begin_layout Standard
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@ -133,7 +124,7 @@ key "kv2001"
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\end_inset
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, licensed to and implemented by K1JT in a closed-source executable for
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, licensed to and implemented by K1JT as a closed-source executable for
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use only in amateur radio applications.
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Since 2001 the KV decoder has been considered the best available soft-decision
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decoder for Reed Solomon codes.
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@ -1121,7 +1112,7 @@ reference "sec:Theory,-Simulation,-and"
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\end_inset
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, we use simulations to set an empirical acceptance threshold
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\begin_inset Formula $r_{0}$
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\begin_inset Formula $r_{1}$
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\end_inset
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that maximizes the probability of correct decodes while ensuring a low
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@ -1145,7 +1136,7 @@ Technically the FT algorithm is a list decoder.
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\begin_inset Formula $d_{s}$
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\end_inset
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are less than conservatively specified limits
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are less than specified limits
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\begin_inset Formula $X_{0}$
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\end_inset
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@ -1162,7 +1153,7 @@ Technically the FT algorithm is a list decoder.
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\begin_inset Formula $r<r_{1}$
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\end_inset
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are used to validate additional decodes that did not pass the first test.
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are used to validate additional codewords that did not pass the first test.
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A timeout is used to limit the algorithm's execution time if no acceptable
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codeword is found in a reasonable number of trials,
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\begin_inset Formula $T$
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@ -1390,17 +1381,17 @@ The FT algorithm is completely general: with equal sensitivity it recovers
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\emph on
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much
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\emph default
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smaller list of messages (say, a few thousand messages or less) that may
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be among the most likely ones to be received.
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smaller list of messages (say, a few thousand messages or less) that we
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can guess may be among the most likely ones to be received.
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One such situation exists when making short ham-radio contacts that exchange
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minimal information including callsigns, signal reports, perhaps Maidenhead
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locators, and acknowledgments.
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On the EME path or on a VHF or UHF band with limited geographical coverage,
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the most likely received messages often originate from callsigns that have
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been decoded before.
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Saving a list of previously decoded callsigns makes it easy to generate
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lists of hypothetical messages and their corresponding codewords, at very
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little computational expense.
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Saving a list of previously decoded callsigns and associated locators makes
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it easy to generate lists of hypothetical messages and their corresponding
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codewords at very little computational expense.
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The resulting candidate codewords can be tested in the same way as those
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generated by the probabilistic method described in Setcion
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\begin_inset CommandInset ref
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@ -1454,16 +1445,8 @@ For hinted decoding we again invoke a ratio threshold test, but in this
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\begin_inset Formula $r_{2},$
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\end_inset
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for what is
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\begin_inset Quotes eld
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\end_inset
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small enough
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\begin_inset Quotes erd
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\end_inset
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to establish adequate confidence, while still ensuring that false decodes
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are rare.
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that is small enough to establish adequate confidence, while still ensuring
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that false decodes are rare.
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Because tested candidate codewords are drawn from a list typically no longer
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than a few thousand, rather than
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\begin_inset Formula $2^{72},$
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@ -1473,22 +1456,14 @@ small enough
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\begin_inset Formula $r_{2}$
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\end_inset
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can set a more relaxed limit than
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\begin_inset Formula $r_{1},$
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can be a more relaxed limit than the
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\begin_inset Formula $r_{1}$
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\end_inset
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as used in the FT algorithm.
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For the limited subset of messages established by operator experience as
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\begin_inset Quotes eld
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\end_inset
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likely,
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\begin_inset Quotes erd
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\end_inset
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hinted decodes can be obtained at lower signal levels than required for
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decodes obtained from the full universe of
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used in the FT algorithm.
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For the limited subset of messages that operator experience suggests to
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be likely, hinted decodes can be obtained at lower signal levels than required
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for those obtained from the full universe of
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\begin_inset Formula $2^{72}$
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\end_inset
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@ -1512,11 +1487,7 @@ Comparisons of decoding performance are usually presented in the professional
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\end_inset
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, the ratio of the energy collected per information bit to the one-sided
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noise power spectral density,
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\begin_inset Formula $N_{0}$
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\end_inset
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.
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noise power spectral density.
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For weak-signal amateur radio work, performance is more conveniently presented
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as the probability of successfully decoding a received word plotted against
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signal-to-noise ratio in a 2500 Hz reference bandwidth,
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@ -1540,12 +1511,12 @@ reference "sec:Appendix:SNR"
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\end_inset
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.
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Examples of both types of plot are included in the following discussion,
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where we describe a number of simulations carried out to compare performance
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of the FT algorithm with others, and with theoretical expectations.
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Examples of both presentations are included in the following discussion,
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where we describe simulations carried out to compare performance of FT
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with other algorithms, and with theoretical expectations.
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We have also used simulations to establish suitable default values for
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the acceptance parameters
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\begin_inset Formula $h_{0},$
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\begin_inset Formula $X_{0},$
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\end_inset
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@ -1556,8 +1527,12 @@ reference "sec:Appendix:SNR"
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\begin_inset Formula $d_{1},$
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\end_inset
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\begin_inset Formula $r_{1},$
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\end_inset
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and
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\begin_inset Formula $r_{1}.$
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\begin_inset Formula $r_{2}.$
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\end_inset
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@ -1582,8 +1557,8 @@ reference "fig:bodide"
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.
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For these tests we generated at least 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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ratio, assuming the additive white gaussian noise (AWGN) channel, and we
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processed the data using each algorithm.
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For word error rates less than 0.1 it was necessary to process 10,000 or
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even 100,000 simulated signals in order to capture enough errors to make
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the measurements statistically meaningful.
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@ -1594,11 +1569,11 @@ reference "fig:bodide"
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\end_inset
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also shows theoretical results for comparison with the BM results.
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also shows results calculated from theory for comparison with the BM results.
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The simulated BM results agree with theory to within about 0.1 dB.
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This difference between simulated BM results and theory is caused by small
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errors in the estimates of time- and frequency-offset of the received signal
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in the simulated results.
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in the simulated data.
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Such
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\begin_inset Quotes eld
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\end_inset
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@ -1615,7 +1590,7 @@ sync losses
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As expected, the soft-decision algorithms, FT and KV, are about 2 dB better
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than the hard-decision BM algorithm.
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In addition, FT has a slight edge (about 0.2 dB) over KV.
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On the other hand, the execution time for FT with
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On the other hand, the execution time for FT with timeout parameter
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\begin_inset Formula $T=10^{5}$
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\end_inset
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@ -1624,7 +1599,7 @@ As expected, the soft-decision algorithms, FT and KV, are about 2 dB better
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\begin_inset Formula $T=10^{5}$
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\end_inset
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is small enough to be practical on most computers.
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is small enough to be practical on most of today's home computers.
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\end_layout
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@ -1694,7 +1669,7 @@ reference "fig:bodide"
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\end_inset
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often extend downward to much smaller error rates, say
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often extend downward to even smaller error rates, say
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\begin_inset Formula $10^{-6}$
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\end_inset
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@ -1711,18 +1686,18 @@ reference "fig:WER2"
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\end_inset
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shows the FT results for
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shows in this format the FT results for
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\begin_inset Formula $T=10^{5}$
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\end_inset
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and the KV results that were shown in Figure
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and the KV results from Figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:bodide"
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\end_inset
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in this format along with additional FT results for
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, along with additional FT results for
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\begin_inset Formula $T=10^{4},\:10^{3},\:10^{2}$
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\end_inset
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@ -1731,14 +1706,13 @@ reference "fig:bodide"
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\end_inset
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.
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The KV results are plotted with open squares.
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It is apparent that the FT decoder produces more decodes than KV when
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\begin_inset Formula $T=10^{4}$
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\end_inset
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or larger.
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It also provides a very significant gain over the hard-decision BM decoder
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even when limited to at most 10 trials.
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even when limited to 10 or fewer trials.
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\end_layout
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\begin_layout Standard
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@ -1794,12 +1768,12 @@ Percent of JT65 messages copied as a function of SNR in 2500 Hz bandwidth.
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\end_layout
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\begin_layout Standard
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The timeout parameter
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Timeout parameter
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\begin_inset Formula $T$
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\end_inset
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employed in the FT algorithm is the maximum number of symbol-erasure trials
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allowed for a particular attempt at decoding a received word.
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is the maximum number of symbol-erasure trials allowed for a particular
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attempt at decoding a received word.
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Most successful decodes take only a small fraction of the maximum allowed
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number of trials.
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Figure
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@ -1810,8 +1784,9 @@ reference "fig:N_vs_X"
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\end_inset
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shows the number of stochastic erasure trials required to find the correct
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codeword versus the number of hard-decision errors in the received word
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for a run with 1000 simulated transmissions at
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codeword vs.
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the number of hard-decision errors in the received word, for a run with
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1000 simulated transmissions at
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\begin_inset Formula $\mathrm{SNR}=-24$
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\end_inset
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@ -1843,7 +1818,7 @@ reference "fig:N_vs_X"
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The variability of the decoding time also increases dramatically with the
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number of errors in the received word.
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These results provide insight into the mean and variance of the execution
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time for the FT algorithm, since execution time will be roughly proportional
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time for the FT algorithm, since execution time is roughly proportional
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to the number of required trials.
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\end_layout
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@ -1928,11 +1903,15 @@ reference "fig:Psuccess"
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We include three curves for each decoding algorithm: one for the AWGN channel
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and no fading, and two more for simulated Doppler spreads of 0.2 and 1.0
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Hz.
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The simulated Doppler spreads are comparable to those encountered on HF
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ionospheric paths and for EME at VHF and lower UHF bands.
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These simulated Doppler spreads are comparable to those encountered on
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HF ionospheric paths and also for EME at VHF and the lower UHF bands.
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For reference, we note that the JT65 symbol rate is about 2.69 Hz.
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(*** A little more description of hinted decoding is needed here, and new
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data for the DS curves.***)
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\end_layout
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\begin_layout Standard
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(*** A little more description is needed here, along with new data for the
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DS curves.***)
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\end_layout
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\begin_layout Standard
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