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Comment by jeffrallen | Hacker News Reader

Definitely, dude. You were much more likely to get a stable and reliable connection from a hardware modem at a slower speed than from a soft modem that was trying for 56 kbits on a bad voice line.

If anyone wants to brush up on their understanding of the Nyquist theorem, give yourself homework to find out why the highest speed ever offered on analog phone lines was 56 kbits. That's a nice Rabbit Hole to tour.

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Channel capacity is b * log2 (1 + snr) where b is the bandwidth in Hz and snr is the linear signal-to-noise ratio.

The voice passband in the old telephone system is 3 kHz. And 60 dB SNR average over the passband was typical for a clear voice channel:

    3000 * log2 1000000 = 59,800 bits per second.

If anyone else is curious now, this is one of the first Google results I found and quite the delightful, in-depth read explaining it:

https://www.10stripe.com/articles/why-is-56k-the-fastest-dia...

Heh, where I lived 56k modems were useless. The telephone infrastructure was already using some kind of cheat where they effectively doubled up the number of voice calls that went over a single wire (and I can't for the life of me remember what this is called now). The most you could ever get would be 28.8, but more likely you'd get 24,000.

You're probably thinking of robbed bit signaling: https://en.wikipedia.org/wiki/Robbed_bit_signaling

This wasn't quite doubling. Five out of six frames were sampled at full 8-bit resolution, while the remaining frame was sampled at 7-bit resolution (hence the "robbed bit"). The "doubling" is probably that you could run 24 digital lines with the 7/8-bit encoding, over the wires used by just two analog phone lines.

Robbed bit signaling was (is) used to encode signaling information on a digital circuit (typically a T1 in North America) without a dedicated signaling channel. There were a variety of multiplexing systems to get more than a single line on a copper pair, but they didn't have anything to do with robbed bit signaling.

The linked forum thread talks about this, its called pair gain.

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