[[PROTOCOL_OVERVIEW]]
=== Overview

All QSO modes except ISCAT use structured messages that compress
user-readable information into fixed-length packets of exactly 72
bits.  Each message consists of two 28-bit fields normally used for
callsigns and a 15-bit field for a grid locator, report,
acknowledgment, or 73.  An additional bit flags a message containing
arbitrary alphanumeric text, up to 13 characters.  Special cases allow
other information such as add-on callsign prefixes (e.g., ZA/K1ABC) or
suffixes (e.g., K1ABC/P) to be encoded. The basic aim is to compress
the most common messages used for minimally valid QSOs into a fixed
72-bit length.

A standard amateur callsign consists of a one- or two-character
prefix, at least one of which must be a letter, followed by a digit
and a suffix of one to three letters. Within these rules, the number
of possible callsigns is equal to 37×36×10×27×27×27, or somewhat over
262 million. (The numbers 27 and 37 arise because in the first and
last three positions a character may be absent, or a letter, or
perhaps a digit.) Since 2^28^ is more than 268 million, 28 bits are
enough to encode any standard callsign uniquely. Similarly, the number
of 4-digit Maidenhead grid locators on earth is 180×180 = 32,400,
which is less than 2^15^ = 32,768; so a grid locator requires 15 bits.

Some 6 million of the possible 28-bit values are not needed for
callsigns.  A few of these slots have been assigned to special message
components such as `CQ`, `DE`, and `QRZ`. `CQ` may be followed by three
digits to indicate a desired callback frequency. (If K1ABC transmits
on a standard calling frequency, say 50.280, and sends `CQ 290 K1ABC
FN42`, it means that s/he will listen on 50.290 and respond there to
any replies.) A numerical signal report of the form `–nn` or
`R–nn` can be sent in place of a grid locator.  (As originally
defined, numerical signal reports `nn` were required to fall between -01
and -30 dB.  Recent program versions accommodate reports between
-50 and +49 dB.) A country prefix or portable suffix may be
attached to one of the callsigns.  When this feature is used the
additional information is sent in place of the grid locator or by
encoding additional information into some of the 6 million available
slots mentioned above.

Finally, the message compression algorithm supports messages starting
with `CQ AA` through `CQ ZZ`.  Such messages are encoded by
sending `E9AA` through `E9ZZ` in place of the first callsign of a
standard message.  Upon reception these calls are converted back to
the form `CQ AA` through `CQ ZZ`.

To be useful on channels with low signal-to-noise ratio, this kind of
lossless message compression requires use of a strong forward error
correcting (FEC) code.  Different codes are used for each mode.
Accurate synchronization of time and frequency is required between
transmitting and receiving stations.  As an aid to the decoders, each
protocol includes a "`sync vector`" of known symbols interspersed with
the information-carrying symbols.  Generated waveforms for all of the
_WSJT-X_ modes have continuous phase and constant envelope.

[[SLOW_MODES]]
=== Slow Modes

[[JT4PRO]]
==== JT4

FEC in JT4 uses a strong convolutional code with constraint length
K=32, rate r=1/2, and a zero tail. This choice leads to an encoded
message length of (72+31) x 2 = 206 information-carrying bits.
Modulation is 4-tone frequency-shift keying (4-FSK) at 11025 / 2520 =
4.375 baud.  Each symbol carries one information bit (the most
significant bit) and one synchronizing bit.  The two 32-bit
polynomials used for convolutional encoding have hexadecimal values
0xf2d05351 and 0xe4613c47, and the ordering of encoded bits is
scrambled by an interleaver.  The pseudo-random sync vector is the
following sequence (60 bits per line):

 000011000110110010100000001100000000000010110110101111101000
 100100111110001010001111011001000110101010101111101010110101
 011100101101111000011011000111011101110010001101100100011111
 10011000011000101101111010


[[JT9PRO]]
==== JT9

FEC in JT9 uses the same strong convolutional code as JT4: constraint
length K=32, rate r=1/2, and a zero tail, leading to an encoded
message length of (72+31) × 2 = 206 information-carrying
bits. Modulation is nine-tone frequency-shift keying, 9-FSK at
12000.0/6912 = 1.736 baud.  Eight tones are used for data, one for
synchronization. Eight data tones means that three data bits are
conveyed by each transmitted information symbol. Sixteen symbol
intervals are devoted to synchronization, so a transmission requires a
total of 206 / 3 + 16 = 85 (rounded up) channel symbols. The sync
symbols are those numbered 1, 2, 5, 10, 16, 23, 33, 35, 51, 52, 55,
60, 66, 73, 83, and 85 in the transmitted sequence.  Tone spacing of
the 9-FSK modulation for JT9A is equal to the keying rate, 1.736 Hz.
The total occupied bandwidth is 9 × 1.736 = 15.6 Hz.

[[JT65PRO]]
==== JT65

A detailed description of the JT65 protocol was published in
{jt65protocol} for September-October, 2005. A Reed Solomon (63,12)
error-control code converts 72-bit user messages into sequences of 63
six-bit information-carrying symbols.  These are interleaved with
another 63 symbols of synchronizing information according to the
following pseudo-random sequence:

 100110001111110101000101100100011100111101101111000110101011001
 101010100100000011000000011010010110101010011001001000011111111


The synchronizing tone is normally sent in each interval having a
"`1`" in the sequence. Modulation is 65-FSK at 11025/4096 = 2.692
baud.  Frequency spacing between tones is equal to the keying rate for
JT65A, and 2 and 4 times larger for JT65B and JT65C.  For EME QSOs the
signal report OOO is sometimes used instead of numerical signal
reports. It is conveyed by reversing sync and data positions in the
transmitted sequence.  Shorthand messages for RO, RRR, and 73 dispense
with the sync vector entirely and use time intervals of 16384/11025 =
1.486 s for pairs of alternating tones. The lower frequency is the
same as that of the sync tone used in long messages, and the frequency
separation is 110250/4096 = 26.92 Hz multiplied by n for JT65A, with n
= 2, 3, 4 used to convey the messages RO, RRR, and 73.

[[QRA64_PROTOCOL]]
==== QRA64

QRA64 is an experimental mode intended for EME and other extreme
weak-signal applications.  Its internal code was designed by IV3NWV.
The protocol uses a (63,12) **Q**-ary **R**epeat **A**ccumulate code
that is inherently better than the Reed Solomon (63,12) code used in
JT65, yielding a 1.3 dB advantage. A new synchronizing scheme is based
on three 7 x 7 Costas arrays.  This change yields another 1.9 dB
advantage. 

In most respects the current implementation of QRA64 is operationally
similar to JT65.  QRA64 does not use two-tone shorthand messages, and
it makes no use of a callsign database.  Rather, additional
sensitivity is gained by making use of already known information as a
QSO progresses -- for example, when reports are being exchanged and
you have already decoded both callsigns in a previous transmission.
QRA64 presently offers no message averaging capability, though that
feature may be added.  In early tests, many EME QSOs were made using
submodes QRA64A-E on bands from 144 MHz to 24 GHz.  

[[SLOW_SUMMARY]]
==== Summary

Table 2 provides a brief summary parameters for the slow modes in
_WSJT-X_.  Parameters K and r specify the constraint length and rate
of the convolutional codes; n and k specify the sizes of the
(equivalent) block codes; Q is the alphabet size for the
information-carrying channel symbols; Sync Energy is the fraction of
transmitted energy devoted to synchronizing symbols; and S/N Threshold
is the signal-to-noise ratio (in a 2500 Hz reference bandwidth) above
which the probability of decoding is 50% or higher.

[[SLOW_TAB]]
.Parameters of Slow Modes
[width="90%",cols="3h,^3,^2,^1,^2,^2,^2,^2,^2,^2",frame=topbot,options="header"]
|===============================================================================
|Mode |FEC Type |(n,k) | Q|Modulation type|Keying rate (Baud)|Bandwidth (Hz)
|Sync Energy|Tx Duration (s)|S/N Threshold (dB)
|JT4A |K=32, r=1/2|(206,72)| 2| 4-FSK| 4.375| 17.5 |
0.50| 47.1 | -23 |JT9A |K=32, r=1/2|(206,72)| 8| 9-FSK| 1.736| 15.6 |
0.19| 49.0 | -27 |JT65A |Reed Solomon|(63,12) |64|65-FSK| 2.692| 177.6
| 0.50| 46.8 | -25 |QRA64A|Q-ary Repeat Accumulate|(63,12) |64|64-FSK|
1.736| 111.1 | 0.25| 48.4 | -26 | WSPR |K=32, r=1/2|(162,50)| 2|
4-FSK| 1.465| 5.9 | 0.50|110.6 | -29
|===============================================================================

Submodes of JT4, JT9, JT65, and QRA64 offer wider tone spacings for
circumstances that may require them, such significant Doppler spread.
Table 3 summarizes the tone spacings, bandwidths, and approximate
threshold sensitivities of the various submodes when spreading is
comparable to tone spacing.

[[SLOW_SUBMODES]]
.Parameters of Slow Submodes
[width="50%",cols="h,3*^",frame=topbot,options="header"]
|=====================================
|Mode  |Tone Spacing  |BW (Hz)|S/N (dB)
|JT4A  |4.375|  17.5  |-23
|JT4B  |8.75 |  30.6  |-22
|JT4C  |17.5 |  56.9  |-21
|JT4D  |39.375| 122.5 |-20
|JT4E  |78.75|  240.6 |-19
|JT4F  |157.5|  476.9 |-18
|JT4G  |315.0|  949.4 |-17
|JT9A  |1.736|  15.6  |-27
|JT9B  |3.472|  29.5  |-26
|JT9C  |6.944|  57.3  |-25
|JT9D  |13.889| 112.8 |-24
|JT9E  |27.778| 224.0 |-23
|JT9F  |55.556| 446.2 |-22
|JT9G  |111.111|890.6 |-21
|JT9H  |222.222|1779.5|-20
|JT65A |2.692| 177.6  |-25
|JT65B |5.383| 352.6  |-25
|JT65C |10.767| 702.5 |-25
|QRA64A|1.736| 111.1  |-26
|QRA64B|3.472| 220.5  |-25
|QRA64C|6.944| 439.2  |-24
|QRA64D|13.889| 876.7 |-23
|QRA64E|27.778|1751.7 |-22
|=====================================

[[FAST_MODES]]
=== Fast Modes

==== ISCAT

ISCAT messages are free-form, up to 28 characters in length.
Modulation is 42-tone frequency-shift keying at 11025 / 512 = 21.533
baud (ISCAT-A), or 11025 / 256 = 43.066 baud (ISCAT-B).  Tone
frequencies are spaced by an amount in Hz equal to the baud rate.  The
available character set is:

----
 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ /.?@-
----

Transmissions consist of sequences of 24 symbols: a synchronizing
pattern of four symbols at tone numbers 0, 1, 3, and 2, followed by
two symbols with tone number corresponding to (message length) and
(message length + 5), and finally 18 symbols conveying the user's
message, sent repeatedly character by character.  The message always
starts with `@`, the beginning-of-message symbol, which is not
displayed to the user.  The sync pattern and message-length indicator
have a fixed repetition period, recurring every 24 symbols.  Message
information occurs periodically within the 18 symbol positions set
aside for its use, repeating at its own natural length.

For example, consider the user message `CQ WA9XYZ`.  Including the
beginning-of-message symbol `@`, the message is 10 characters long.
Using the character sequence displayed above to indicate tone numbers,
the transmitted message will therefore start out as shown in the first
line below:

----
 0132AF@CQ WA9XYZ@CQ WA9X0132AFYZ@CQ WA9XYZ@CQ W0132AFA9X ...
 sync##                  sync##                 sync##
----

Note that the first six symbols (four for sync, two for message
length) repeat every 24 symbols.  Within the 18 information-carrying
symbols in each 24, the user message `@CQ WA9XYZ` repeats at its own
natural length, 10 characters.  The resulting sequence is extended as
many times as will fit into a Tx sequence.

==== JT9

The JT9 slow modes all use keying rate 12000/6912 = 1.736 baud.  By contrast, with
the *Fast* setting submodes JT9E-H adjust the keying rate to match the
increased tone spacings.  Message durations are therefore much
shorter, and they are sent repeatedly throughout each Tx sequence.
For details see Table 4, below.

==== MSK144

Standard MSK144 messages are structured in the same way as those in
the slow modes, with a 72 bits of user information.  Forward error
correction is implemented by first augmenting the 72 message bits with
an 8-bit cyclic redundancy check (CRC) calculated from the message
bits. The CRC is used to detect and eliminate most false decodes at
the receiver. The resulting 80-bit augmented message is mapped to a
128-bit codeword using a (128,80) binary low-density-parity-check
(LDPC) code designed by K9AN specifically for this purpose.  Two 8-bit
synchronizing sequences are added to make a message frame 144 bits
long.  Modulation is Offset Quadrature Phase-Shift Keying (OQPSK) at
2000 baud. Even-numbered bits are conveyed over the in-phase channel,
odd-numbered bits on the quadrature channel.  Individual symbols are
shaped with half-sine profiles, thereby ensuring a generated waveform
with constant envelope, equivalent to a Minimum Shift Keying (MSK)
waveform.  Frame duration is 72 ms, so the effective character
transmission rate for standard messages is up to 250 cps.

MSK144 also supports short-form messages that can be used after QSO
partners have exchanged both callsigns.  Short messages consist of 4
bits encoding a signal report, R+report, RRR, or 73, together with a
12-bit hash code based on the ordered pair of "`to`" and "`from`"
callsigns.  Another specially designed LDPC (32,16) code provides
error correction, and an 8-bit synchronizing vector is appended to
make up a 40-bit frame.  Short-message duration is thus 20 ms, and
short messages can be decoded from very short meteor pings.

The 72 ms or 20 ms frames of MSK144 messages are repeated without gaps
for the full duration of a transmission cycle. For most purposes, a
cycle duration of 15 s is suitable and recommended for MSK144.

The modulated MSK144 signal occupies the full bandwidth of a SSB
transmitter, so transmissions are always centered at audio frequency
1500 Hz. For best results, transmitter and receiver filters should be
adjusted to provide the flattest possible response over the range
300Hz to 2700Hz. The maximum permissible frequency offset between you
and your QSO partner ± 200 Hz.

==== Summary

.Parameters of Fast Modes
[width="90%",cols="3h,^3,^2,^1,^2,^2,^2,^2,^2",frame="topbot",options="header"]
|=====================================================================
|Mode     |FEC Type   |(n,k)   | Q|Modulation Type|Keying rate (Baud)
|Bandwidth (Hz)|Sync Energy|Tx Duration (s)
|ISCAT-A  |   -       |  -     |42|42-FSK| 21.5 |  905  | 0.17| 1.176 
|ISCAT-B  |   -       |  -     |42|42-FSK| 43.1 | 1809  | 0.17| 0.588 
|JT9E     |K=32, r=1/2|(206,72)| 8| 9-FSK| 25.0 |  225  | 0.19| 3.400 
|JT9F     |K=32, r=1/2|(206,72)| 8| 9-FSK| 50.0 |  450  | 0.19| 1.700 
|JT9G     |K=32, r=1/2|(206,72)| 8| 9-FSK|100.0 |  900  | 0.19| 0.850 
|JT9H     |K=32, r=1/2|(206,72)| 8| 9-FSK|200.0 | 1800  | 0.19| 0.425 
|MSK144   |LDPC       |(128,72)| 2| OQPSK| 2000 | 2400  | 0.11| 0.072 
|MSK144 Sh|LDPC       |(32,16) | 2| OQPSK| 2000 | 2400  | 0.20| 0.020 
|=====================================================================
