V.32terbo: technical details¶

V.32terbo's specification was never published, so this page records what D-Modem's version (in dsp/dp_v32.cpp) is based on. For an overview, see V.32terbo.

Where it comes from¶

Public sources say little beyond the speeds: AT&T, 1993, 16800 and 19200 bit/s, 2400 baud, an 1800 Hz carrier, trellis coding. No patent, datasheet, Usenet post or open-source modem found gives the rate bits, the constellations or the coding.

The Agere soft modem in the interop tests (dsp/test/agere/agrsm_core.o, Agere SoftModem 2.1.40) has all of it. Agere came out of AT&T Microelectronics through Lucent, so its V.32 code is AT&T's line of V.32terbo. The object file is not stripped, and its symbols name each piece:

Its V.32bis maps (cCoded7200Map to cCoded14400Map) are exactly D-Modem's V.32bis constellations times 14, point for point, which confirms how its tables are indexed and scaled. The modem's own +MS takes V32T, and its connection type list has v.32/v.32bis/v.32terbo.

The interop tests then check the result against the modem itself (below).

The rate signals¶

The R and E words are V.32bis's. V.32bis leaves bits B13 and B14 of them reserved (sent as 0); V.32terbo uses them:

Both need B8 (trellis coding) as well, like V.32bis's trellis rates. Agere's E for 19200 is F993 (B0 first: B0 to B4, B7, B8, B11, B14, B15), for 16800 F995. A modem offering V.32terbo sends its R with B13 and B14 set; a V.32bis modem ignores them and answers with a V.32bis rate, so the start-up needs nothing else.

Coding and constellations¶

The 8 state trellis code of V.32bis, unchanged. 16800 bit/s carries 7 data bits a symbol (Q1 Q2 through the coder, Q3 to Q7 uncoded), 19200 carries 8 (Q3 to Q8 uncoded): 256 and 512 point constellations, indexed as V.32bis's are (Y0, then Y1 Y2, then the uncoded bits). The points lie on the usual odd-sum integer grid: steps of 10/14 of V.32bis's grid for 16800 (coordinates up to 12), half steps for 19200 (up to 18). Both have about V.32bis's mean power. Within each of the 8 subsets the points are 4 grid steps apart (squared distance 16), as in V.32bis.

The tables are in dsp/qam_tables.cpp.

The non-linear encoder¶

At 16800 and 19200 every point is warped before it is sent: points far from the centre are pushed further out, those near it pulled in a little. This spreads the outer points, which suffer most from the companding noise of the digital phone network's G.711 coding. V.34 later standardized the same idea (its non-linear encoder, 9.7/V.34).

Agere's fixed-point code, at its transmit scale (one V.32bis grid unit is 2048), does, for a point Y:

s  = ((|Y|^2 >> 14) * 20649) >> 14
c  = (s * s) >> 15
b  = (c * s) >> 15
e  = (2731 s + 137 c + 3 b) >> 12
g  = ((e * 15027) >> 17) + 15027
Y' = (Y * g) >> 14

In other words Y' = 0.917 Y (1 + z/6 + z^2/120 + z^3/5040), with z = 0.0098 |Y|^2 in V.32bis grid units: the series of sinh(sqrt z)/sqrt z. Its decoder applies the inverse series. D-Modem computes the warped points once (in dsp/qam_tables.cpp, with the same integer steps) and uses them as the constellation: the transmitter sends them and the Viterbi decoder measures distances to them directly.

Both modems must use the same transmit scale for the warp to match. V32EncoderEnableHighScaleFactor (a scale 1.414 times larger) is turned on by V32ControlReset early in the start-up and off again when the rate signals begin, so data uses the normal scale. The interop test confirms it: D-Modem decodes the Agere modem's 19200 bit/s with its own warped table at a mean squared error of 0.0005 of the signal's power.

Receiving 512 points¶

V.32bis's receiver needed two changes to take 19200 bit/s; both apply to all the trellis rates:

• The gain is held in data mode. The AGC follows the signal's power over about 30 ms. On a dense constellation that estimate wanders by a few per cent, which moves the outer points by as much as the spacing of the 512 point constellation. In data mode the gain is now frozen and the equalizer follows slow changes. Back to back, data's SNR went from about 31 dB to 40 dB on a clean line.
• B1 is used to train. Data begins with 128 symbols of scrambled ones (B1). The receiver knows its descrambler's register, so it knows exactly what the remote sends then, except for the remote's trellis encoder state, which no standard fixes (Agere's starts in state 31, ours in 0). It follows all 32 states for 8 symbols, picks the one that matches, and trains on the true points for the rest of B1. With only decisions to go on, the equalizer at 19200 sometimes settled on a gain 1 to 2 per cent off, which the outer points cannot take.

The rate each modem asks for comes from its training's error. That estimate tops out near 31 dB, so the thresholds were set from back to back runs: 19200 from an estimate of 29.5 dB, 16800 from 26.5 dB. On pump_test's line that picks 19200 from 34 dB of SNR and 16800 from 26 dB; forced, 19200 runs clean from about 32 dB and 16800 from 24 dB.

Not done¶

• Rate renegotiation. V.32bis's rate renegotiation is not implemented for any of the V.32 family; D-Modem retrains instead.
• V.8. V.8 has no code for V.32terbo; it is used only when chosen with AT+MS=V32T.

Tests¶

• pump_test: v32terbo* (clean, 27 dB, no band limit, 8000 Hz, 300 ppm clock offset, an echo), and V32Terbo.Rates (19200 at 40 dB, 16800 at 27 dB, 14400 at 25 dB, each without a bit error).
• agere_232_agere_calls, agere_232_open_calls: the Agere modem and D-Modem, both with AT+MS=V32T, call each other and connect at 19200 bit/s both ways (ctest -L agere).