How Many Bits Are Copied in a JT65 Transmission?
Joe Taylor, K1JT
Recent evidence suggests that some in the EME community are confused about whatis actually copied over the radio path when using the JT65 communication protocol. Although the full technical details of JT65 have been published elsewhere,1 and source codefor the program WSJT is openly available,2 those resources may seem overly technical for
non-specialists in communication theory. This brief note is intended to help WSJT users andnonusers alike to understand what happens during the processes of transmitting, receiving,and decoding a JT65 signal. I have taken special care to use language, units of measurement, and terms of reference familiar to amateurs using traditional weak-signal coding andmodulation techniques.
User Information, Encoding, and Channel Symbols
Standard JT65 messages contain 72 bits of user information—typically two 28-bit callsigns,3 a 15-bit grid locator, and one bit to indicate the message type. A Reed Solomon(63,12) error-correcting code translates the 72 message bits into 63 six-bit “channel symbols.” Thus, every transmission includes 6 × 63 = 378 information-carrying bits and has aredundancy ratio of 378/72 = 5.25. It is important to understand that the user message is
not transmitted in its “natural” sequence of syllables or characters (as it would be in normal
speech, Morse code or ASCII data, for example). Instead, the user information is mathematically encoded so that it is spread throughout the entire sequence of 63 symbols. This fact
has profound implications when comparing JT65 with traditional modes. First, the distribution of redundant information is designed so as to maximize the potential recovery of thefull message content, even when the signal-to-noise ratio (SNR) is so low that many symbols
from the transmitted sequence are lost in the noise. Second, a brief signal dropout of a few
seconds will have quite diﬀerent eﬀects in JT65 compared with a traditional sequential mode.
In a sequential mode, the dropout will simply result in the loss of those characters that werebeing transmitted at the time. But in JT65 encoding, the brief loss of signal will not aﬀect
any part of the message in particular; the impact is statistical, aﬀecting recoverability ofthe entire message. These fundamental diﬀerences make it diﬃcult to directly compare theperformance of JT65 and traditional sequential modes.
1

J. Taylor, K1JT, “The JT65 Communications Protocol”, QEX, September-October 2005, pp. 3–12.

2

Source code can be downloaded from http://developer.berlios.de/projects/wsjt/.

3

The number of licensed amateur radio operators is less than 222 (roughly 4.2 million), so in principle 22
bits would be enough to encode a callsign. JT65 uses 28 bits for this task, however, so I adopt the latter
number throughout this paper.

1After a JT65 message has been encoded into its 63 channel symbols, the symbols aretransmitted one by one using 64-tone frequency shift keying (FSK). A 65th audio tone, twotone-intervals below the lowest data tone, is used to facilitate accurate synchronization oftime and frequency between transmitter and receiver. The overall modulation scheme canthus be described as 65-FSK. Half of the transmitted energy is devoted to the essential taskof synchronization: during each 46.8 s transmission, 63 sync-tone intervals are inserted at
speciﬁed locations among the 63 data tones, following a prescribed pseudo-random pattern.
Pictorial representations of the spectrograms of two JT65 transmissions are presented
in Figure 1. Time increases from left to right in the ﬁgure, and frequency from bottom to topof each panel. Each black dot corresponds to a transmitted tone. For each transmission, 63of the tones convey the encoded channel symbols, while the remaining 63 (along the bottomof each panel) are the sync tone. The upper spectrum represents the message “VK7MO
K1JT FN20”, while the lower one is “VK7MP K1JT FN20”. Only one character in themessage has changed, but 52 of the 63 channel symbols are diﬀerent. This fact illustrates theextraordinary power of the RS(63,12) code used in JT65: the sequences of channel symbols
for any two of the 272 possible JT65 messages can never have more than 11 symbol values
in common. This is the reason that complete messages can be received exactly as sent, evenwhen many channel symbols have been corrupted or lost in the noise.
[Figure 1 near here.]
Analysis of a Received JT65 Signal
WSJT begins the analysis of a JT65 signal by identifying the sync tone and using it toestablish its frequency oﬀset (relative to the nominal 1270.5 Hz) and the time oﬀset caused bypropagation delay and computer clock errors. Spectral analysis is then carried out for eachof the 63 intervals containing the information-carrying channel symbols. This process yields
measurements of signal power for each symbol, divided into 64 frequency bins. The bin withlargest power yields the most probable value of the symbol being received at that moment;
the second largest corresponds to the second most probable symbol value, and so on, down
to the smallest. Thus, the information conveyed by each symbol is partly contained in its
most probable value, but additional information is contained in a series of other possible
values, with progressively decreasing probabilities of being correct. Each correctly received
symbol conveys 6 of the 378 transmitted bits.
Study of Figure 1 should make it clear that there is no obvious correspondence between
individual characters in a message and particular values or locations in the encoded sequenceof channel symbols. As stated earlier, all of the message information is mixed together andmathematically distributed over the entire sequence. A correctly received message may result
from as few as 12 channel symbols received with high conﬁdence, or all 63 symbols received
with relatively low individual conﬁdence, or any of a wide range of possibilities between these2

two extremes. The spectra of JT65 signals received over the air will diﬀer from the idealized
ones shown in Figure 1 because they include random noise and fading signals. The statisticalproperties of signal and noise variations will determine the levels of conﬁdence assigned toindividual symbol values.
Hard and Soft Symbols
As an educational exercise for myself, and to help answer for everyone the question
posed in the title, I have carried out a series of explicit measurements of the number ofcorrectly copied channel symbols in JT65 transmissions. One thousand simulated transmissions were generated at each SNR between 0 and −40 dB in 2500 Hz bandwidth, in 1 dBsteps. These transmissions were received and analyzed, and the number of correctly copied
symbols determined for each one. The averaged results for each signal level are plotted as
the solid curve in Figure 2. The probability of correct symbol reception depends only on
signal-to-noise ratio; it is independent of details of any decoding algorithms that might beused subsequently, in a program like WSJT, to convert the raw channel symbols into callsigns
or other user information.
[Figure 2 near here.]
Up to this point, discussion of the reception of channel symbols has been limited to“hard” decisions: a symbol’s value has been taken as the index of its frequency bin withthe highest measured power. However, signiﬁcant additional information is contained in theactual values of the power measurements, which can be used to indicate which symbols are
the most reliable and to produce “soft symbol” probabilities. At low SNR, many symbols
that were not correctly received as the most probable value will be correct as the second mostprobable, and others as the third, fourth, and so on. Relatively few correct symbol values
will be found among the lowest-ranking probabilities. To provide quantitative examples ofthis type of information, the dashed and dotted curves in Figure 2 illustrate the average
number of received symbols for which the correct value was found in the top 2, 4, or 8 of
the 64 spectral power measurements. An ideal decoding procedure takes advantage of all
soft-decision information through the full range of probabilities.
Decoding the Message
Figure 2 shows that at SNRs down to −20 dB, JT65 signals transfer an average ofmore than 39 correct hard-decision channel symbols from transmitter to receiver. With theReed Solomon (63,12) code used in JT65, 38 correct symbols are always enough to guarantee
complete reception of a 72-bit user message with high conﬁdence, even if only a hard-decision
decoder is used. If the locations of symbols likely to be unreliable are known—those during
a signal fadeout, for example—these can be ﬂagged as “erasures,” and a smaller number ofcorrect symbols will then suﬃce for decoding. Better still, true soft-symbol information may
3be used. WSJT is packaged with a compiled version of the Koetter-Vardy algebraic softdecision decoding algorithm,4 which takes partial advantage of probabilistic information on
the most probable and second most probable values of every symbol. The KV algorithm candecode single JT65 transmissions down to about −25 dB, again with very high conﬁdence
in the result.
As can be seen in Figure 2, at still lower signal levels the number of correctly copied
channel symbols decreases. The hard-decision number falls to 9.3 (the equivalent of two
JT65 callsigns) slightly below −28 dB. This signal level is close to the typical lower limit fordecoding by the JT65 Deep Search (DS) algorithm, which will be described next.
An ideal JT65 decoder would create two-dimensional arrays like those depicted in Figure 1 for all possible messages, and would cross-correlate each one of them with the corresponding soft-symbol array for the received signal. Any JT65 message diﬀerent from theone actually transmitted would produce 11 or fewer matching channel symbols, whereas thecorrect message would exhibit (soft) matches for all 63. The correlation procedure would
make use of the full soft-information content, and a quantitative indication of the resulting
conﬁdence level would be provided for any decoded message. Unfortunately, an exhaustive
search of every possible JT65 message is not computationally feasible. However, since thelist of active EME stations is no more than a few thousand, and since activity patternschange rather slowly with time, it is perfectly feasible for WSJT to carry out an exhaustive
search for callsigns in that relatively short list. Such a procedure is the basis of the JT65
Deep Search algorithm.
When using the DS decoder, WSJT forms a large number of hypotheses about whatmessage a JT65 signal might contain, based on the receiving station’s call and the contents
of a callsign database. Each hypothesis is tested to see whether the received symbols match
those of the hypothetical encoded message. This algorithm can be programmed to result in
the high-conﬁdence decoding of any one of the hypothesized messages, but no others. An
exhaustive search is the optimal decoding strategy, in the sense of achieving the best possible
decoder performance. When practicable, it is usually the method of choice.
Levels of Confidence
The number of hypothetical messages tested during a JT65 Deep Search is typicallybetween 14,000 and 20,000. The decoder’s task is to determine whether one of these messages
matches the transmitted one to some speciﬁed level of conﬁdence, or to establish that noneof them does. To illustrate how this process works, Figure 3 shows examples of correlations
4

R. Koetter and A. Vardy, “Soft-Decision Algebraic Decoding of Reed Solomon Codes,” in IEEE Transactions on Information Theory, 49, 2809–2825, 2003.

4

obtained when doing the simulations reported in this paper. The top panel is for signal-tonoise ratio −26 dB, and the bottom for −28 dB. Dots represent correlations of the noisy,
fading signals against the message actually transmitted, for 1000 diﬀerent simulations at
each signal level. Crosses show correlations against incorrect messages selected at random
from the group of all possible JT65 messages. It is easy to see that with a threshold set
at about 3 correlation units, the decoder can make sure that nearly all transmissions at−28 dB and higher will be decoded correctly and that there will be very few false decodes.
Recent versions of WSJT produce numerical conﬁdence levels on an arbitrary 0 to 10 scalemonotonically related to the scale used in Figure 3. Roughly speaking, level 3 on WSJT’s
scale implies moderately high conﬁdence, and anything over 6 implies high or very highconﬁdence. In normal practice the operator will have other relevant information available,
so WSJT requires the operator to make all ﬁnal decisions about valid copy.
Summary and Conclusions
To provide succinct answers to the question posed in the title, a subset of the measurements obtained in the simulations is summarized in Table 1. Entries are included for SNRs
between −18 and −28 dB, at 2 dB intervals, and for convenience the results are quoted
in channel symbols, bits, and equivalent 28-bit callsigns. Even at the lowest usable signal
levels, around −28 dB, the number of hard-decision bits correctly copied over the radio pathexceeds the number required to convey two callsigns. The numbers in Table 1 are conservative lower limits, because they are based on hard decisions only. Soft-decision information
adds signiﬁcantly to the totals and further enhances the sensitivity as well as the levels of
conﬁdence that can be assigned to decoded messages.
Table 1. Hard-decision channel symbols copied over the air, per JT65 transmission.

SNR Channel(dB) symbols
−18
46.9
−20
39.6
−22
31.9
−24
23.1
−26
15.5
−28
9.6

Bits
281
237
191
139
93
58

Equivalent
callsigns
10.1
8.4
6.9
4.9
3.3
2.1

The information presented here should lay to rest any fears that when using its Deep
Search decoder, JT65 might not transfer enough channel symbols over the radio path tosatisfy traditional requirements for valid QSOs. It is certainly true that at the lowest usable
5signal levels, between −25 and −28 dB on the WSJT scale, some prior information about
active stations is required for the Deep Search decoder to succeed. Of course, prior information of this type is advantageous when trying to make a diﬃcult contact or identify aweak station calling CQ, using any mode, for exactly the same reason—it gives the decoder,consciously or otherwise, some idea of what message content to look for. Helpful lists of“good calls” have been a part of contesting and weak signal amateur communications for
decades. It has never been considered illegitimate to possess or make use of such informationin the process of copying a weak signal, as long as the copy is truly accomplished. Figure 2
and Table 1 show that this condition is easily met by JT65.
In an article recently published5 in DUBUS, Klaus von der Heide, DJ5HG, presented ananalysis of the decoders used in WSJT with the goal of promoting an objective discussionof what constitutes a minimum valid QSO. Using the formalism of information theory, heshowed that the KV decoder meets a “strict” deﬁnition of a QSO, while the DS decoder
meets a “dynamic” deﬁnition. The diﬀerence between the two is that the strict deﬁnition
requires that all necessary information be treated as unknown at the start of a QSO, while
the dynamic deﬁnition acknowledges that some information (such as one’s own callsign)
may be known, and still other information might be found in a list. Traditional practice has
always accommodated the inevitable knowledge of one’s own callsign, and has also acceptedthat lists and schedules do not invalidate QSOs. A mode like JT65 that uses compressed,
structured messages cannot account for individual parts of a message such as characters incallsigns, because they are not transmitted as such. One can still insist, however, that a
suﬃcient number of channel symbols be copied over the air, and that operator conﬁdence inthe decoded message meets a suitably high standard. The measurements described in thispaper show that the JT65 Deep Search decoder passes these tests easily—and therefore that
it, too, produces valid QSOs in terms of traditional amateur practice.
The article by DJ5HG quite properly calls attention to the fact that the number ofdistinct messages decodable by the Deep Search algorithm is no larger than several times
the length of the callsign database. Information theory says that if all hypothetical messages
constructed from that database are assumed equally likely, the quantity of transferred user
information can be taken as the base-2 logarithm of the number of decodable messages.
The resulting number of bits—approximately 14.2 for the default Deep Search setup of
WSJT—is a useful and valid measure of the previously unknown information transferred
when such a message is decoded. In a scheduled QSO, whatever the modulation mode,
the number of transferred, previously unknown bits may be even smaller. However, thesemeasures of the quantity of transferred information should not be confused with the numberof probabilistically evaluated, information-carrying symbols or bits conveyed over the radio5

K. von der Heide, DJ5HG, “Minimal QSOs and Their Validity,” DUBUS, 35, No 1, pp. 38–53, 2006.

6path from transmitter to receiver. The latter quantities—those illustrated in Figure 2 andTable 1 of this paper—are roughly analogous to characters or other fragments copied froma marginal CW signal. They carry proportionally more weight in JT65, however, because of
the strong error-correcting code and because the process of synchronization ﬁxes the exact
location of each symbol within the transmitted sequence. Signal strength variations provide
the JT65 decoders with important probabilistic information about which received symbols
are the most reliable. Together, these factors lead to the very high level of QSO integritythat is achieved with JT65.

7

Frequency

Time

Fig. 1.— Idealized spectrograms of the JT65 transmissions for “VK7MO K1JT FN20” (top) and“VK7MP K1JT FN20” (bottom). The horizontal axis represents 46.8 s of time; the vertical axisof each panel represents frequency over the range of 65 tones used by JT65. Black marks indicate
transmitted tones, corresponding to the encoded channel symbols. The pseudo-random patternalong the bottom of each panel is the synchronizing tone. Note that although the two messages
are nearly identical, the patterns of channel symbols are almost entirely diﬀerent (except for thepattern of the synchronizing tone, which is always the same).

8Fig. 2.— Measurements of the number of correctly copied channel symbols over a simulated radio
path, plotted as a function of SNR on the WSJT scale and assuming 64-FSK modulation andnoncoherent detection. Generated JT65 signals were degraded by Rayleigh fading and by additive
white Gaussian noise. The solid curve (labeled “1”) gives hard-decision results; the remaining
curves provide some indication of the soft-decision information by showing the average number oftimes that the correct symbol fell in the top 2, 4, or 8 of the 64 measurements of spectral power.
Adjustments were made to the curves to remove the biasing eﬀects of accidentally correct symbol
values. The dotted horizontal line shows the equivalent number of bits in two 28-bit callsigns.

9

Fig. 3.— Examples of correlation values produced by the Deep Search decoder for four diﬀerent
groups of 1000 simulated transmissions. The signal-to-noise ratios were set at −26 dB (upper) and−28 dB (lower), on the WSJT scale. Dots represent correlations against correct messages, whilecrosses represent incorrect messages. A decoding threshold set at about 3.0 would assure thatnearly all transmissions above −28 dB will be decoded correctly, with few decoding errors.

10