The 39-tone parallel mode (MIL-STD-188-110 appendix B)

hfmodem.bateleur.tone39 sends and receives the 39-tone parallel waveform of MIL-STD-188-110B appendix B (the same text as 110A's appendix B), 75 to 2400 bit/s. It was written from the appendix. No other implementation was read. Four published recordings of other senders were used as test partners only: they are not in the tree, and nothing was taken from them but which way the text's open choices go.

The waveform (appendix B)

Where the text leaves a choice open, the published recordings settled it. Each tone's phase is reckoned from the start of its own element. Figure B-5's register is read with its labels. A symbol's first bit sent is its most significant. The module's docstring says which recording settled which.

The receiver

Acquisition looks for part one's four tones, searched on a grid ±80 Hz wide. It takes them when they hold a quarter of the energy on average over half of part one. Noise gives a few hundredths and data under a tenth. The tones' phase advance over part one then gives the carrier offset to a fraction of a hertz.

The element timing comes from which tones each element holds: part one's four, part two's three, then part three's and the data's forty. Part one's and two's tones are data tones as well, so they are left out of that last set, and each boundary reads in both directions. Energy is used, not phase: across two paths the tones' phases part company, and a match that summed them lost the timing by an element or two even at 30 dB.

That timing is good to within the guard. settle then centres it. The changes from element to element don't care where in the guard the window starts, so how cleanly they fall on the QDPSK points is flat across every timing the paths allow. The middle of that plateau is taken, when the curve stands out from the noise.

Where the data starts is settled by the framing that opens it, not by counting the preamble's parts. Senders lay those parts out differently: one recording has an extra all-tone element before its data, another one between parts one and two. A start one element late still reads as framing, because the framing runs for several elements. But the framing it measures is then short of every tabulated length, so the start whose framing is as long as a table says is taken.

Offsets and clocks.

• Carrier offset. Each element is reckoned from its own start, so an offset turns every change by 2π·df·T, about 8° a hertz. That is known, and past 5.5 Hz it is beyond what the fourth power can resolve, so it is taken off before.
• Clock error. The sender's clock is measured from the whole message: a clock error turns each tone's changes in proportion to its frequency. The fourth power removes the data, and the slope across the tones gives the clock to about 20 ppm through fading. Each element is then read where it falls, the sub-sample remainder corrected in phase. Without this, 300 ppm (a poor sound card) loses a 30 s message. With it, 800 ppm through the 2 ms / 2 Hz channel decodes. Two guards constrain the estimate. It is measured only over the elements the transmission is on (the data tones' median power against the empty places), not the Morse identification after it: one steady tone read as a clock of −89 000 ppm. And it is taken only when the slope stands three standard errors clear of none: a short message at 4 dB through fading showed −538 ppm that was not there, and lost its last 20 bytes to it.
• Gross clock errors. One recording is 0.76% fast. Part one's four tones, spread over 2 kHz, show that, and the audio is resampled when the data then reads better. Fading scatters that estimate by several hundred ppm, so it is used only past 1500.

Decoding. A (7,3) word is the code word nearest the soft bits, all 4096 of them weighed at once. A (14,10) word that doesn't check is searched for among erasures of its least reliable nibbles, two at a time with an error or four at a time, and the nearest candidate found is taken. Against hard decisions and two erasures this took 1200 bit/s at 15 dB from 4e-4 to no errors.

The mode isn't carried in the preamble, so it is detected:

1. The framing sequence's length and the tones it arrives on give the rate and diversity.
2. The first super block's code words give the interleaving degree.
3. How the characters are framed decides between synchronous and asynchronous: per B.5.7, or as some senders leave them (start SPACE, stop MARK).
4. Text decides the character width.

A sender working from another edition's tables: one recording frames 75 bit/s with 384 bits, a length no table here has. Its framing length is measured from the sequence's end, and the degree is found from the code words (Mode39(..., seq=384), named 75/4/S:384).

Late entry

Appendix B defines no late-entry procedure as such. It makes one possible: B.5.4.3 puts the framing sequence back into the data every few super blocks (table B-III), and from each insertion the data runs on exactly as it did from the first. tone39.late_entry (and offair decode 39 --late --mode <mode>) joins a transmission whose preamble was missed:

• the offset comes from the Doppler tone, a line well over its empty neighbourhood below the first data tone;
• the element timing comes from the data. A window across an element's edge mixes two elements' phases, so its changes sit less tightly on the constellation. The receiver fits the run of windows that lie wholly inside an element;
• the framing sequence is looked for at every bit of the demodulated stream, since in some asynchronous 2400 bit/s modes an insertion begins inside an element. Decoding then starts there, as it would after the preamble.

The mode must be known. How long joining can take is the mode's insertion interval: 2.4 s at 2400 bit/s with degree 9, 9.4 s at 1200 bit/s with degree 63, 20 s at 600 bit/s with degree 33, and a minute and a half to two and a half minutes at 75 bit/s.

Tested against itself at 1200, 600 (CCIR poor) and 2400 bit/s, synchronous and asynchronous. It is offline only: the streaming receiver still needs the preamble.

Simulation measurements

The recorded short harness was rerun in simulation on 2026-09-30 with corrected Gaussian-spectrum Rayleigh fading. Each row uses one trial, one second of requested payload (minimum 16 bytes), message seed 1000 and channel seed 0. Preambles, interleaver fill and flush extend the waveform beyond the requested payload duration. SNR is measured in 3 kHz; the carrier offset is +23 Hz unless shown otherwise. Two-path channels have independent equal-power taps. Spread is twice the Gaussian spectral standard deviation. Every missing bit counts as an error.

Bounds below are one-sided 95% binomial upper bounds assuming independent bit errors. Fading errors are correlated, so these are conditional bounds. The short trials do not establish a standards performance target.

The earlier long-run B-XII summaries lacked per-trial records and a source revision; their fading figures are withdrawn. In the corrected short run, 1200L at 15 dB changed from 0 to 2 errors in 1,200 bits: BER 0.00166667, conditional upper bound 0.00523711 instead of 0.00249333. Both errors were in delivered data; no bits were missing. The other six rows retained zero errors and unchanged conditional bounds.

A separate existing clock regression also changed in simulation. At 600/33/S, two equal paths 2 ms apart with 2 Hz spread, 10 dB SNR in 3 kHz, +7 Hz offset, −300 ppm clock error and channel seed 1, a 13,440-bit repeated payload changed from 0 to 2 errors, with no missing bits. Its conditional upper bound rose from 0.000222872 to 0.000468362. The clock estimate changed from −261.01 to −245.06 ppm, exceeding the test's 40 ppm tolerance. Neither run detected EOM. This regression remains open; the test assertion is unchanged.

Reproduce these simulation rows:

python -m hfmodem.bateleur.measure --preset b-xii --trials 1 --seconds 1 --output b-xii-short.json

Omitting the short-run overrides requests sixteen 20-second payloads per row; the counts above do not describe that longer run. See bateleur's simulation measurements for the channel correction and the recorded fields.

Recordings

On the station

The modem always listens for it (stream.Receiver39), on the front end's real audio at 9600 Hz: the 1800 Hz matched filter the serial waveforms use would cut the Doppler tone. With MODE 39 <mode> set, a transmission is decoded in that mode as soon as its timing is found; with none, the mode is found from the data once about eight seconds of it are in (detect_elements). Elements are read as they arrive, each where the sender's clock puts it: the clock is measured every 128 elements over the last 384, and the reading moves half way to it. tests/bateleur/test_stream.py holds the streaming receiver to the offline one, 400 ppm included. Transmitting, the modem reckons how long a message keys from element_count, without rendering it, and splits one too long for max_key_s.

The SNR reported is the data tones' power against the four empty places between the Doppler tone and the first data tone (450–619 Hz), over the elements the message was decoded from: within a dB or two of the channel's.

Not done

• Late entry on the station: the streaming receiver needs the preamble; joining under way is offline only (late_entry).
• Gross clock errors (past 1500 ppm, a recording played at the wrong speed) are put right offline only; the streaming receiver follows what a sound card does.
• The extended preamble is sent and received but was tested only in loopback.

The streaming receiver searches both preamble lengths without an external extended-preamble flag. Asynchronous transmission uses MARK stop bits, as in the cited 2400 bit/s recordings. A caller sending seven data bits can supply parity in the high bit of each input byte; the receiver still accepts both observed stop conventions. The continuous Doppler pilot starts the data at the phase reached by the end of preamble part three. A bandpass filter limits short-burst skirts; its 400-sample tail is included in duration.