mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-25 13:48:42 -05:00
A few (last-minute?) edits and corrections.
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6444 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor
parent
a232d9da9d
commit
c00c0d1921
@ -163,8 +163,8 @@ JT65 uses timed transmitting and receiving sequences one minute long.
|
||||
Messages are short and structured so as to streamline minimal exchanges
|
||||
between two amateur operators over potentially difficult radio paths.
|
||||
Most messages contain two callsigns and a grid locator, signal report,
|
||||
acknowledgment, or sign-off; one of the tokens ``CQ'', ``QRZ'', or ``DE''
|
||||
may be substituted for the first callsign.
|
||||
acknowledgment, or sign-off; one of the tokens CQ, QRZ, or DE may be substitute
|
||||
d for the first callsign.
|
||||
Alternatively, a message may contain up to 13 Latin characters of arbitrary
|
||||
text.
|
||||
All messages are efficiently compressed into exactly 72 bits of digital
|
||||
@ -182,7 +182,11 @@ key "jt65_protocol"
|
||||
|
||||
.
|
||||
For a concise description of the overall process of transmitting and receiving
|
||||
a JT65 message, see the accompanying sidebar.
|
||||
a JT65 message, see the accompanying sidebar
|
||||
\series bold
|
||||
JT65 Message Processing
|
||||
\series default
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -211,7 +215,8 @@ ly.
|
||||
The JT65 code is properly described as a short block-length, low-rate Reed-Solo
|
||||
mon code based on a 64-symbol
|
||||
\emph on
|
||||
alphabet
|
||||
alphabet.
|
||||
|
||||
\emph default
|
||||
|
||||
\begin_inset CommandInset nomenclature
|
||||
@ -221,7 +226,6 @@ description "A sequence of possible symbol values used for signaling. JT65 uses
|
||||
|
||||
\end_inset
|
||||
|
||||
.
|
||||
Characters in this alphabet are mapped onto 64 different frequencies for
|
||||
transmission.
|
||||
|
||||
@ -230,8 +234,8 @@ description "A sequence of possible symbol values used for signaling. JT65 uses
|
||||
\begin_layout Standard
|
||||
Reed Solomon codes are widely used to ensure reliability in data transmission
|
||||
and storage.
|
||||
In hardware implementations, decoding is generally accomplished with an
|
||||
algorithm such as the Berlekamp-Massey (BM) algorithm, based on
|
||||
In hardware implementations, decoding is generally accomplished with a
|
||||
procedure such as the Berlekamp-Massey (BM) algorithm, based on
|
||||
\emph on
|
||||
hard decisions
|
||||
\emph default
|
||||
@ -299,7 +303,7 @@ MAP65
|
||||
WSJT-X
|
||||
\emph default
|
||||
, widely used for amateur weak-signal communication using JT65 and other
|
||||
specialized digital modes.
|
||||
specialized digital protocols.
|
||||
These programs are open-source, freely available
|
||||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
@ -313,13 +317,13 @@ key "wsjt"
|
||||
\begin_layout Standard
|
||||
The JT65 protocol specifies transmissions that 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 available time encourages
|
||||
experimentation with decoders of high computational complexity.
|
||||
As a result, the FT algorithm can extend the decoding threshold on a typical
|
||||
fading channel by many dB over the hard-decision BM decoder, and by a meaningfu
|
||||
l amount over the KV decoder.
|
||||
Receiving software therefore has as much as ten seconds to decode a message
|
||||
before the start of the next minute, when the operator will send a reply.
|
||||
With today's personal computers, this relatively long time encourages experimen
|
||||
tation with decoders of high computational complexity.
|
||||
With time to spare, the FT algorithm lowers the decoding threshold on a
|
||||
typical fading channel by many dB over the hard-decision BM decoder, and
|
||||
by a meaningful amount over the KV decoder.
|
||||
In addition to its excellent performance, the new algorithm has other desirable
|
||||
properties, not least of which is its conceptual simplicity.
|
||||
Decoding performance and computational complexity scale in a convenient
|
||||
@ -339,13 +343,13 @@ The remainder of this paper is organized as follows.
|
||||
Section 3 provides statistical motivation for the FT algorithm, and Section
|
||||
4 describes the algorithm in full detail.
|
||||
Material in these two sections is important because it documents our approach
|
||||
and underlines its fundamental technical contribution.
|
||||
It is heavier in formal mathematics than common in
|
||||
and underlines its fundamental technical contributions.
|
||||
These sections are heavier in formal mathematics than common in
|
||||
\emph on
|
||||
QEX
|
||||
\emph default
|
||||
; for this reason, some readers may choose to skip or skim sections 3 and
|
||||
4 and proceed more quickly to the results.
|
||||
; for this reason, some readers may choose to skip or skim them and proceed
|
||||
more quickly to the results.
|
||||
Most readers will benefit by reviewing the original paper on the JT65 protocol
|
||||
|
||||
\begin_inset CommandInset citation
|
||||
@ -377,8 +381,11 @@ WSJT-X
|
||||
\emph default
|
||||
.
|
||||
Section 7 summarizes some on-the-air experiences with the new decoder.
|
||||
You may Refer to the sidebar Glossary for brief definitions of some specialized
|
||||
terms.
|
||||
Refer to the sidebar
|
||||
\series bold
|
||||
Glossary
|
||||
\series default
|
||||
for brief definitions of some specialized terms.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Section
|
||||
@ -427,7 +434,7 @@ description "For the JT65 code, a vector of 63 symbol values each in the range 0
|
||||
\end_inset
|
||||
|
||||
, the number of message symbols conveyed by the codeword; and the transmission
|
||||
alphabet or number of possible values for each symbol in the codewords.
|
||||
alphabet, or number of possible values for each symbol in the codewords.
|
||||
The codeword length and the number of message symbols are specified with
|
||||
the notation
|
||||
\begin_inset Formula $(n,k)$
|
||||
@ -474,8 +481,8 @@ description "The Hamming distance between two codewords, or between a received w
|
||||
|
||||
\end_inset
|
||||
|
||||
is used as a measure of the lack of agreement between different codewords,
|
||||
or between a received word
|
||||
is used as a measure of disagreement between different codewords, or between
|
||||
a received word
|
||||
\begin_inset CommandInset nomenclature
|
||||
LatexCommand nomenclature
|
||||
symbol "{\\bf Received word: }"
|
||||
@ -486,7 +493,7 @@ description "A vector of symbol values, possibly accompanied by soft information
|
||||
and a codeword.
|
||||
Hamming distance is the number of code symbols that differ in two words
|
||||
being compared.
|
||||
Reed-Solomon codes have minimum Hamming distance
|
||||
Reed-Solomon codes have guaranteed minimum Hamming distance
|
||||
\begin_inset Formula $d$
|
||||
\end_inset
|
||||
|
||||
@ -513,7 +520,7 @@ With
|
||||
.
|
||||
With 72 information bits in each message, JT65 can transmit any one of
|
||||
|
||||
\begin_inset Formula $2^{72}$
|
||||
\begin_inset Formula $2^{72}\approx4.7\times10^{21}$
|
||||
\end_inset
|
||||
|
||||
possible messages.
|
||||
@ -522,8 +529,12 @@ With
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
A received word containing some incorrect symbols (errors) can be decoded
|
||||
into the correct codeword using a deterministic
|
||||
A received word containing some
|
||||
\emph on
|
||||
errors
|
||||
\emph default
|
||||
(incorrect symbols) can be decoded into the correct codeword using a determinis
|
||||
tic,
|
||||
\begin_inset CommandInset nomenclature
|
||||
LatexCommand nomenclature
|
||||
symbol "{\\bf Deterministic algorithm: }"
|
||||
@ -531,7 +542,7 @@ description "A series of computational steps that for the same input always prod
|
||||
|
||||
\end_inset
|
||||
|
||||
, algebraic algorithm provided that no more than
|
||||
algebraic algorithm provided that no more than
|
||||
\begin_inset Formula $t$
|
||||
\end_inset
|
||||
|
||||
@ -561,7 +572,7 @@ For the JT65 code
|
||||
\end_inset
|
||||
|
||||
errors.
|
||||
In the unlikely event that the location of every error is known and if
|
||||
In the unlikely event that the location of every error is known, and if
|
||||
no correct symbols are accidentally labeled as errors, the BM algorithm
|
||||
can correct up to
|
||||
\begin_inset Formula $d-1=n-k$
|
||||
@ -801,9 +812,9 @@ GNU Octave
|
||||
\emph default
|
||||
as function
|
||||
\family typewriter
|
||||
hygepdf
|
||||
hygepdf(x,N,X,s)
|
||||
\family default
|
||||
(x,N,X,s).
|
||||
.
|
||||
The cumulative probability that at least
|
||||
\begin_inset Formula $\epsilon$
|
||||
\end_inset
|
||||
@ -979,7 +990,7 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase
|
||||
\begin_inset Formula $N=53$
|
||||
\end_inset
|
||||
|
||||
less reliable symbols.
|
||||
less reliable ones.
|
||||
If
|
||||
\begin_inset Formula $s=45$
|
||||
\end_inset
|
||||
@ -1075,8 +1086,8 @@ Example 3 shows how statistical information about symbol quality should
|
||||
Once erasure probabilities have been assigned to each of the 63 received
|
||||
symbols, the FT algorithm uses a random number generator to decide whether
|
||||
or not to erase each symbol, according to its assigned erasure probability.
|
||||
The list of erased symbols is then submitted to the BM decoder which either
|
||||
produces a codeword or fails to decode.
|
||||
The list of erased symbols is then submitted to the BM decoder, which produces
|
||||
either a codeword or a flag indicating failure to decode.
|
||||
|
||||
\end_layout
|
||||
|
||||
@ -1091,20 +1102,16 @@ candidate
|
||||
\emph default
|
||||
.
|
||||
Our next task is to find a metric that can reliably select one of many
|
||||
proffered candidates as the codeword actually transmitted.
|
||||
proffered candidates as the codeword that was actually transmitted.
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
The FT algorithm uses quality indices made available by a noncoherent 64-FSK
|
||||
demodulator (see the sidebar
|
||||
\begin_inset Quotes eld
|
||||
\end_inset
|
||||
|
||||
JT65 Information Processing
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
\series bold
|
||||
JT65 Message Processing
|
||||
\series default
|
||||
).
|
||||
The demodulator computes binned power spectra for each signaling interval;
|
||||
the result is a two-dimensional array
|
||||
@ -1149,7 +1156,7 @@ JT65 Information Processing
|
||||
\begin_inset Formula $p_{1}$
|
||||
\end_inset
|
||||
|
||||
-rank, the rank
|
||||
-rank (the rank
|
||||
\begin_inset Formula $\{1,2,\ldots,63\}$
|
||||
\end_inset
|
||||
|
||||
@ -1161,13 +1168,14 @@ JT65 Information Processing
|
||||
\begin_inset Formula $p_{1}$
|
||||
\end_inset
|
||||
|
||||
values, and the ratio
|
||||
values) and the ratio
|
||||
\begin_inset Formula $p_{2}/p_{1}$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
Note that high ranking symbols have larger signal-to-noise ratio than those
|
||||
with lower rank; and when
|
||||
High ranking symbols have larger signal-to-noise ratio than those with
|
||||
lower rank.
|
||||
When
|
||||
\begin_inset Formula $p_{2}/p_{1}$
|
||||
\end_inset
|
||||
|
||||
@ -1176,13 +1184,21 @@ JT65 Information Processing
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
We use 3-bit quantization of these two metrics to index the entries in an
|
||||
|
||||
We use 3-bit quantization of the metrics
|
||||
\begin_inset Formula $p_{1}$
|
||||
\end_inset
|
||||
|
||||
-rank and
|
||||
\begin_inset Formula $p_{2}/p_{1}$
|
||||
\end_inset
|
||||
|
||||
to index the entries in an
|
||||
\begin_inset Formula $8\times8$
|
||||
\end_inset
|
||||
|
||||
table of symbol error probabilities derived empirically from a large data
|
||||
set of received words that were successfully decoded.
|
||||
table of symbol error probabilities.
|
||||
The probabilities were derived empirically from a large data set of received
|
||||
words that were successfully decoded.
|
||||
The table provides an estimate of the
|
||||
\emph on
|
||||
a priori
|
||||
@ -1196,7 +1212,7 @@ a priori
|
||||
\end_inset
|
||||
|
||||
.
|
||||
This table is a key element of the algorithm, as it will define which symbols
|
||||
This table is a key element of the algorithm, as it determines which symbols
|
||||
are effectively protected from erasure.
|
||||
The
|
||||
\emph on
|
||||
@ -1296,8 +1312,8 @@ In practice we find that
|
||||
\begin_inset Formula $u$
|
||||
\end_inset
|
||||
|
||||
, the average signal-plus-noise power in all symbols according to a candidate
|
||||
codeword's symbol values:
|
||||
, the average signal-plus-noise power in all received symbols according
|
||||
to a candidate codeword's symbol values:
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -1345,7 +1361,7 @@ The correct JT65 codeword produces a value for
|
||||
\end_inset
|
||||
|
||||
for the correct codeword has expectation value (average over many random
|
||||
realizations)
|
||||
realizations) given by
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -1422,11 +1438,7 @@ i.e.
|
||||
\end_inset
|
||||
|
||||
where the subscript
|
||||
\begin_inset Quotes eld
|
||||
\end_inset
|
||||
|
||||
i
|
||||
\begin_inset Quotes erd
|
||||
\begin_inset Formula $i$
|
||||
\end_inset
|
||||
|
||||
is an abbreviation for
|
||||
@ -1480,7 +1492,7 @@ If
|
||||
\begin_inset Formula $y$
|
||||
\end_inset
|
||||
|
||||
is too small for decoding to be possible, or the correct codeword is never
|
||||
is too small for decoding to be possible or the correct codeword is never
|
||||
presented as a candidate, the ratio
|
||||
\begin_inset Formula $r=u_{2}/u_{1}$
|
||||
\end_inset
|
||||
@ -1547,9 +1559,9 @@ As with all decoding algorithms that generate a list of possible codewords,
|
||||
\begin_inset Formula $r<R_{1}$
|
||||
\end_inset
|
||||
|
||||
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,
|
||||
are used to validate additional codewords that fail the first test.
|
||||
A timeout is used to limit execution time if no acceptable codeword is
|
||||
found in a reasonable number of trials,
|
||||
\begin_inset Formula $T$
|
||||
\end_inset
|
||||
|
||||
@ -1563,8 +1575,11 @@ As with all decoding algorithms that generate a list of possible codewords,
|
||||
\end_inset
|
||||
|
||||
or even higher.
|
||||
Pseudo-code for the FT algorithm is presented in an accompanying box as
|
||||
Algorithm 1.
|
||||
Pseudo-code for the FT algorithm is presented in an accompanying box,
|
||||
\series bold
|
||||
Algorithm 1
|
||||
\series default
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -1661,7 +1676,7 @@ If
|
||||
\begin_inset Formula $d_{1}=d_{s},$
|
||||
\end_inset
|
||||
|
||||
and
|
||||
|
||||
\begin_inset Formula $X_{1}=X,$
|
||||
\end_inset
|
||||
|
||||
@ -1744,15 +1759,8 @@ key "lc2004"
|
||||
|
||||
.
|
||||
After developing this algorithm, we became aware that our approach is conceptua
|
||||
lly similar to a
|
||||
\begin_inset Quotes eld
|
||||
\end_inset
|
||||
|
||||
stochastic erasures-only list decoding algorithm
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
described in reference
|
||||
lly similar to the stochastic, erasures-only list decoding algorithm described
|
||||
in reference
|
||||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "ls2009"
|
||||
@ -1767,11 +1775,11 @@ key "ls2009"
|
||||
|
||||
\end_inset
|
||||
|
||||
is applied to higher-rate Reed-Solomon codes on a symmetric channel with
|
||||
is applied to higher-rate Reed-Solomon codes on a symmetric channel using
|
||||
binary phase-shift keying (BPSK).
|
||||
Our 64-ary input channel with 64-FSK modulation required us to develop
|
||||
unique methods for assigning erasure probabilities and for defining acceptance
|
||||
criteria to select the best codeword from the list of candidates.
|
||||
criteria to select the best codeword from the list of tested candidates.
|
||||
|
||||
\end_layout
|
||||
|
||||
@ -1870,11 +1878,11 @@ not
|
||||
\end_inset
|
||||
|
||||
possible messages.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
Pseudo-code for the hinted decode or Deep Search algorithm is presented
|
||||
as Algorithm 2.
|
||||
Pseudo-code for the hinted-decoding algorithm is presented as
|
||||
\series bold
|
||||
Algorithm 2
|
||||
\series default
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -1958,18 +1966,17 @@ Otherwise, declare decoding failure and exit.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Enumerate
|
||||
An acceptable hinted decode has been found.
|
||||
Declare a successful result and return the saved codeword and the value
|
||||
|
||||
An acceptable codeword has been found.
|
||||
Declare a successful result and return the codeword and the value
|
||||
\begin_inset Formula $q=100\,(u_{1}-bu_{2})$
|
||||
\end_inset
|
||||
|
||||
as a confidence indicator.
|
||||
By default we use the value
|
||||
(By default we use the value
|
||||
\begin_inset Formula $b=1.12$
|
||||
\end_inset
|
||||
|
||||
for submode JT65A.
|
||||
for submode JT65A.)
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
@ -2095,16 +2102,16 @@ sync losses
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
As expected, the soft-decision algorithms FT and KV are about 2 dB better
|
||||
than the hard-decision BM algorithm on the AWGN channel.
|
||||
As expected, on the AWGN channel 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 about 0.2 dB at
|
||||
higher SNRs to nearly 0.5 dB at low SNR.
|
||||
Execution time for FT with timeout parameter
|
||||
With timeout parameter
|
||||
\begin_inset Formula $T=10^{5}$
|
||||
\end_inset
|
||||
|
||||
is longer than that for the KV algorithm, but still small enough to be
|
||||
practical on today's home computers.
|
||||
execution time for FT is longer than that for the KV algorithm, but still
|
||||
small enough to be fully practical on today's home computers.
|
||||
|
||||
\end_layout
|
||||
|
||||
@ -2197,7 +2204,7 @@ reference "fig:WER2"
|
||||
|
||||
\end_inset
|
||||
|
||||
shows the FT and KV results from Figure
|
||||
replots the FT and KV results from Figure
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand ref
|
||||
reference "fig:bodide"
|
||||
@ -2235,8 +2242,12 @@ reference "fig:bodide"
|
||||
\end_inset
|
||||
|
||||
dB gain over KV at low SNR.
|
||||
It also provides very significant gains over the hard-decision BM decoder
|
||||
even when limited to very small numbers of trials.
|
||||
It also provides very significant gains over the hard-decision BM decoder,
|
||||
even when limited to very small
|
||||
\begin_inset Formula $T$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
@ -2312,7 +2323,7 @@ reference "fig:N_vs_X"
|
||||
\end_inset
|
||||
|
||||
shows the number of stochastic erasure trials required to find the correct
|
||||
codeword as a function of
|
||||
codeword plotted as a function of
|
||||
\begin_inset Formula $X,$
|
||||
\end_inset
|
||||
|
||||
@ -2440,13 +2451,26 @@ reference "fig:Psuccess"
|
||||
Hz.
|
||||
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 comparison we note that the JT65 symbol rate is about 2.7 Hz.
|
||||
For comparison we note that the JT65 symbol rate is about
|
||||
\begin_inset ERT
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
|
||||
|
||||
\backslash
|
||||
linebreak
|
||||
\end_layout
|
||||
|
||||
\end_inset
|
||||
|
||||
2.7 Hz.
|
||||
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 Deep Search (DS) decoding.
|
||||
Simulated Doppler spreads of 0.2 Hz actually increased the FT decoding rate
|
||||
slightly at SNRs close to the decoding threshold, presumably because with
|
||||
the low-rate JT65 code signal peaks provide the information needed for
|
||||
the low-rate JT65 code, signal peaks provide the information needed for
|
||||
good copy.
|
||||
\end_layout
|
||||
|
||||
@ -2486,10 +2510,10 @@ Percentage of JT65 messages successfully decoded as a function of
|
||||
Franke-Taylor (FT) decoding algorithms.
|
||||
Curves labeled DS correspond to the hinted-decode (Deep Search) algorithm
|
||||
with a codeword list of length
|
||||
\begin_inset Formula $L=5850$
|
||||
\begin_inset Formula $L\,$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
= 5850.
|
||||
Numbers adjacent to the curves are simulated Doppler spreads in Hz.
|
||||
In the current version of
|
||||
\emph on
|
||||
@ -2523,12 +2547,16 @@ The JT65 protocol has proven remarkably versatile.
|
||||
Today the mode is used by thousands of amateurs around the world, communicating
|
||||
over terrestrial paths on the MF and HF bands and over terrestrial as well
|
||||
as EME paths from 50 MHz through 10 GHz.
|
||||
Three submodes are in use, together accommodating a wide range of Doppler
|
||||
spreads and potential instrumental instabilities.
|
||||
Three
|
||||
\emph on
|
||||
submodes
|
||||
\emph default
|
||||
are in use, together accommodating a wide range of Doppler spreads and
|
||||
potential instrumental instabilities.
|
||||
All three submodes transmit the 63 data symbols interspersed with 63 synchroniz
|
||||
ation symbols at keying rate 11025/4096 = 2.69 baud.
|
||||
Submode JT65A uses tone spacing equal to the symbol rate, so its total
|
||||
occupied bandwidth is
|
||||
Submode JT65A uses tone spacing equal to the symbol rate; its total occupied
|
||||
bandwidth is
|
||||
\begin_inset Formula $66\times2.69=177.6$
|
||||
\end_inset
|
||||
|
||||
@ -2602,7 +2630,7 @@ name "fig:JT65B_EME"
|
||||
|
||||
Examples of JT65B EME signals recorded at K1JT.
|
||||
Numbers above the spectrogram are audio frequencies in Hz, and the spectrogram'
|
||||
s vertical direction is one minute of time.
|
||||
s vertical span is one minute of time.
|
||||
The horizontal green bar on the frequency axis indicates the bandwidth
|
||||
occupied by the second decoded signal, a reply from SP6GWB.
|
||||
See text for additional details.
|
||||
@ -2629,7 +2657,7 @@ reference "fig:spectrogram"
|
||||
shows activity in submode JT65A during a single minute on the 20 m amateur
|
||||
band.
|
||||
At this time the band was crowded with overlapping signals.
|
||||
You can probably count at least 19 distinct synchronizing tones (the speckled
|
||||
With care you can count at least 19 distinct synchronizing tones (the speckled
|
||||
vertical lines in the figure), and can see that in some places as many
|
||||
as four signals overlap.
|
||||
After signal processing to demodulate the signals and produce soft-symbol
|
||||
@ -2679,8 +2707,12 @@ name "fig:spectrogram"
|
||||
|
||||
\end_inset
|
||||
|
||||
Spectrogram showing one minute of data collected under crowded band conditions
|
||||
on the 20 m band.
|
||||
Spectrogram from
|
||||
\emph on
|
||||
WSJT-X
|
||||
\emph default
|
||||
showing one minute of data collected under crowded band conditions on the
|
||||
20 m band.
|
||||
Numbers on the scale are frequencies (in Hz) above 14.076 MHz.
|
||||
|
||||
\end_layout
|
||||
@ -2849,7 +2881,7 @@ key "lhmg2010"
|
||||
|
||||
\end_inset
|
||||
|
||||
"Stochastic Chase Decoding of Reed-Solomon Codes", Camille Leroux, Saied
|
||||
``Stochastic Chase Decoding of Reed-Solomon Codes'', Camille Leroux, Saied
|
||||
Hemati, Shie Mannor, Warren J.
|
||||
Gross,
|
||||
\emph on
|
||||
@ -2868,8 +2900,8 @@ key "lk2008"
|
||||
|
||||
\end_inset
|
||||
|
||||
"Soft-Decision Decoding of Reed-Solomon Codes Using Successive Error-and-Erasure
|
||||
Decoding," Soo-Woong Lee and B.
|
||||
``Soft-Decision Decoding of Reed-Solomon Codes Using Successive Error-and-Erasur
|
||||
e Decoding,'' Soo-Woong Lee and B.
|
||||
V.
|
||||
K.
|
||||
Vijaya Kumar,
|
||||
@ -2893,11 +2925,7 @@ key "ls2009"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
Stochastic Erasure-Only List Decoding Algorithms for Reed-Solomon Codes,
|
||||
``Stochastic Erasure-Only List Decoding Algorithms for Reed-Solomon Codes,
|
||||
\begin_inset Quotes erd
|
||||
\end_inset
|
||||
|
||||
@ -3122,7 +3150,9 @@ height_special "totalheight"
|
||||
status open
|
||||
|
||||
\begin_layout Paragraph
|
||||
Sidebar: JT65 Information Processing
|
||||
|
||||
\size large
|
||||
Sidebar: JT65 Message Processing
|
||||
\end_layout
|
||||
|
||||
\begin_layout Enumerate
|
||||
|
||||
Loading…
Reference in New Issue
Block a user