mirror of https://github.com/saitohirga/WSJT-X.git
Mostly minor editing. I think it's mostly done now, except for Section 7.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6368 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor
parent
e61e8c5d81
commit
e0f40f71fc
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@ -117,7 +117,7 @@ A major reason for the success and popularity of JT65 is its use of a strong
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error-correction code: a short block-length, low-rate Reed-Solomon code
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based on a 64-symbol alphabet.
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Until now, nearly all programs implementing JT65 have used the patented
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Koetter-Vardy (KV) algebraic soft-decision decoder
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Kötter-Vardy (KV) algebraic soft-decision decoder
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\begin_inset CommandInset citation
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LatexCommand cite
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key "kv2001"
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@ -155,9 +155,8 @@ The JT65 protocol specifies transmissions that normally start one second
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into a UTC minute and last for 46.8 seconds.
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Receiving software therefore has up to several seconds to decode a message
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before the start of the next minute, when the operator sends a reply.
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With today's personal computers, this relatively long time available for
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decoding a short message encourages experimentation with decoders of high
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computational complexity.
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With today's personal computers, this relatively long available time encourages
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experimentation with decoders of high computational complexity.
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As a result, on a typical fading channel the FT algorithm can extend the
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decoding threshold by many dB over the hard-decision Berlekamp-Massey decoder,
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and by a meaningful amount over the KV decoder.
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@ -247,7 +246,7 @@ The minimum Hamming distance of the JT65 code is
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\end_inset
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, which means that any particular codeword differs from all other codewords
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in at least 52 symbol positions.
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in at least 52 or the 63 symbol positions.
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\end_layout
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@ -1326,10 +1325,10 @@ If
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\end_inset
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and
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\begin_inset Formula $X_{1}=X.$
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\begin_inset Formula $X_{1}=X,$
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\end_inset
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and save the codeword.
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\end_layout
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\begin_layout Enumerate
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@ -1375,7 +1374,7 @@ Otherwise, declare decoding failure and exit.
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\begin_layout Enumerate
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An acceptable codeword has been found.
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Declare a successful decode and return this codeword.
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Declare a successful decode and return the saved codeword.
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\end_layout
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\end_inset
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@ -1416,7 +1415,7 @@ stochastic erasures-only list decoding algorithm
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\begin_inset Quotes erd
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\end_inset
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, described in reference
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described in reference
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\begin_inset CommandInset citation
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LatexCommand cite
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key "ls2009"
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@ -1462,14 +1461,14 @@ much
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\emph default
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smaller list of messages (say, a few thousand messages or less) that we
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might suppose would 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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One such favorable situation exists when making short ham-radio contacts
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that exchange minimal information including callsigns, signal reports,
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perhaps Maidenhead locators, and acknowledgments.
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On the EME path or a VHF or UHF band with limited geographical coverage,
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the most common 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 and associated locators makes
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it easy to generate lists of hypothetical messages and their corresponding
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it easy to generate a list 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 almost the same way
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as those generated by the probabilistic method described in Section
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@ -1507,7 +1506,12 @@ For hinted decoding we again invoke a ratio threshold test, but in this
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case we use it to answer a more limited question.
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Over the full list of messages considered likely, we want to know whether
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a suitable metric can distinguish with confidence between the one correct
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codeword and all others in the generated list.
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codeword and all others in the generated list --- or, alternatively, to
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determine that the correct codeword is
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\emph on
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not
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\emph default
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contained in the list.
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We again find that the most effective metric involves a comparison of
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\begin_inset Formula $u_{1}$
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\end_inset
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@ -1521,12 +1525,12 @@ For hinted decoding we again invoke a ratio threshold test, but in this
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The criterion for comparison is chosen empirically to maximize the number
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of correct decodes while ensuring 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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than a few thousand entries, rather than
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\begin_inset Formula $2^{72},$
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\end_inset
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the limit can can be more relaxed than that used in the FT algorithm.
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THus, for the limited subset of messages suggested by operator experience
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Thus, for the limited subset of messages suggested by previous experience
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to be likely, hinted decodes can be obtained at lower signal levels than
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required for the full universe of
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\begin_inset Formula $2^{72}$
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@ -1535,6 +1539,18 @@ For hinted decoding we again invoke a ratio threshold test, but in this
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possible messages.
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\end_layout
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\begin_layout Standard
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Pseudo-code for the hinted decode or
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\begin_inset Quotes eld
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\end_inset
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Deep Search
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\begin_inset Quotes erd
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\end_inset
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algorithm is presented in an accompanying text box.
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\end_layout
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\begin_layout Standard
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\begin_inset Float algorithm
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wide false
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@ -1584,14 +1600,14 @@ If
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\end_inset
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by setting
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\begin_inset Formula $u_{2}=u_{1},$
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\begin_inset Formula $u_{2}=u_{1}.$
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\end_inset
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then set
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\begin_inset Formula $u_{1}=u.$
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Then set
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\begin_inset Formula $u_{1}=u$
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\end_inset
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and save the codeword.
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\end_layout
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\begin_layout Enumerate
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@ -1611,12 +1627,22 @@ If
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\end_layout
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\begin_layout Enumerate
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Otherwise, declare hinted-decoding failure and exit.
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Otherwise, declare decoding failure and exit.
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\end_layout
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\begin_layout Enumerate
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An acceptable hinted decode has been found.
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Declare a successful result and return this codeword.
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Declare a successful result and return the saved codeword and the value
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\begin_inset Formula $q=100*(u_{1}-bu_{2})$
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\end_inset
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as a confidence indicator.
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By default we use
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\begin_inset Formula $b=1.12$
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\end_inset
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.
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\end_layout
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\end_inset
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@ -1667,7 +1693,7 @@ reference "sec:Appendix:SNR"
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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 simulations carried out to compare performance of FT
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with other algorithms and with theoretical expectations.
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and hinted decoding 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 $X_{0},$
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@ -1723,11 +1749,11 @@ reference "fig:bodide"
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\end_inset
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also shows results calculated from theory for comparison with the BM results.
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also shows results calculated from theoretical probability distributions
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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 data.
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This differences are caused by small errors in the estimates of time and
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frequency offset of the received signal 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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@ -1741,7 +1767,7 @@ sync losses
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\end_layout
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\begin_layout Standard
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As expected, the soft-decision algorithms, FT and KV, are about 2 dB better
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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 an edge over KV that increases from
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\begin_inset Formula $\sim0.2$
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@ -1928,7 +1954,11 @@ name "fig:WER2"
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\end_inset
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Percent of JT65 messages copied as a function of SNR in 2500 Hz bandwidth.
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Percent of JT65 messages copied as a function of
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\begin_inset Formula $\mathrm{SNR}{}_{2500},$
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\end_inset
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assuming additive white gaussian noise and no fading.
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Numbers adjacent to curves specify values of timeout parameter
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\begin_inset Formula $T$
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\end_inset
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@ -1976,11 +2006,11 @@ reference "fig:N_vs_X"
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the number of hard-decision errors in the received word.
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This run used 1000 simulated transmissions at
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\begin_inset Formula $\mathrm{SNR}=-24$
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\begin_inset Formula $\mathrm{SNR_{2500}}=-24$
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\end_inset
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dB, just slightly above the decoding threshold, and the timeout parameter
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was
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dB, just slightly above the decoding threshold, with timeout parameter
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\begin_inset Formula $T=10^{5}.$
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\end_inset
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@ -2004,8 +2034,8 @@ reference "fig:N_vs_X"
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symbol errors.
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The results also show that, on average, the number of trials increases
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with the number of errors in the received word.
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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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The variability of decoding time also increases dramatically with the number
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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 is roughly proportional
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to the number of required trials.
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@ -2044,9 +2074,8 @@ Number of trials needed to decode a received word versus Hamming distance
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\end_inset
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between the received word and the decoded codeword, for 1000 simulated
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frames on an AWGN channel with no fading.
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The SNR in 2500 Hz bandwidth is
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\begin_inset Formula $-24$
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transmissions on an AWGN channel with no fading and
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\begin_inset Formula $\mathrm{SNR}{}_{2500}=-24$
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\end_inset
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dB, which corresponds to
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@ -2101,18 +2130,21 @@ reference "fig:Psuccess"
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\begin_layout Standard
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It is interesting to note that while Rayleigh fading severely degrades the
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success rate of the BM decoder, the penalties are much smaller with both
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FT and hinted decoding.
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FT and
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\begin_inset Quotes eld
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\end_inset
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Deep Search
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\begin_inset Quotes erd
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\end_inset
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decoding.
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Simulated Doppler spreads of 0.2 Hz actually increased the FT and DS decoding
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rates slightly at SNRs close to the decoding threshold, presumably because
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with the low-rate JT65 code signal peaks can be enough to produce good
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copy.
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\end_layout
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\begin_layout Standard
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(*** New data will be used for the DS curves.
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***)
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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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@ -2140,11 +2172,14 @@ name "fig:Psuccess"
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\end_inset
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Percentage of JT65 messages successfully decoded as a function of SNR in
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2500 Hz bandwidth.
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Percentage of JT65 messages successfully decoded as a function of
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\begin_inset Formula $\mathrm{SNR}{}_{2500}$
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\end_inset
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.
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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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Curves labeled DS correspond to the hinted-decode (
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Curves labeled DS correspond to the hinted-decode or
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\begin_inset Quotes eld
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\end_inset
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@ -2152,8 +2187,8 @@ Deep Search
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\begin_inset Quotes erd
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\end_inset
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) algorithm.
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Numbers adjacent to the curves are the simulated Doppler spreads in Hz.
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algorithm.
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Numbers adjacent to the curves are simulated Doppler spreads in Hz.
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The curve labeled
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\begin_inset Quotes eld
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\end_inset
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@ -2162,8 +2197,8 @@ Sync
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\begin_inset Quotes erd
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\end_inset
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illustrates the rate of correct time and frequency synchronization in the
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decoder presently implemented in program
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illustrates the success rate of correct time and frequency synchronization
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in the decoder presently implemented in program
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\emph on
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WSJT-X
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\emph default
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@ -2247,7 +2282,7 @@ key "kv2001"
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\end_inset
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“Algebraic soft-decision decoding of Reed-Solomon codes,” R.
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Köetter and A.
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Kötter and A.
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Vardy,
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\emph on
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IEEE Transactions on Information Theory
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@ -2276,6 +2311,22 @@ WSJT Home Page
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\begin_inset CommandInset bibitem
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LatexCommand bibitem
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label "3"
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key "lc2004"
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\end_inset
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\emph on
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Error Control Coding, 2nd Edition
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\emph default
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, Shu Lin and Daniel J.
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Costello, Pearson-Prentice Hall, 2004.
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\end_layout
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\begin_layout Bibliography
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\begin_inset CommandInset bibitem
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LatexCommand bibitem
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label "4"
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key "lhmg2010"
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\end_inset
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@ -2294,7 +2345,7 @@ IEEE Communications Letters
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\begin_layout Bibliography
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\begin_inset CommandInset bibitem
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LatexCommand bibitem
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label "4"
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label "5"
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key "lk2008"
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\end_inset
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@ -2313,25 +2364,7 @@ GLOBECOM
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\begin_inset Quotes erd
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\end_inset
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2008 proceedings
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\emph default
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.
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\end_layout
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\begin_layout Bibliography
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\begin_inset CommandInset bibitem
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label "5"
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key "lc2004"
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\end_inset
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\emph on
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Error Control Coding, 2nd Edition
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\emph default
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, Shu Lin and Daniel J.
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Costello, Pearson-Prentice Hall, 2004.
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2008 proceedings.
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\end_layout
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\begin_layout Bibliography
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