[computator]

> if your ISP-side modem directly outputs digital audio, the downstream channel capacity is significantly higher

But why is it higher? It's still an analog channel (the last mile from the ISP to your house), right? Doesn't it get filtered? So isn't it still subject to the Shannon-Nyquist limit?

Here's an ASCII drawing of which parts are digital vs analog as I understood your explanation:

  Rest of world<--- digital--->Telco<---digital--->ISPmodem<---analog--->HomeModem

Suppose you're saying that the link between the ISPmodem and the HomeModem is a bare unfiltered copper wire. In that case, I have a different question: Couldn't you send data at megabits per seconds over a mile long copper wire without using modems at all (using just UARTs?).

I hope you can clear up my confusion.

[ycombiredd]

> Couldn't you send data at megabits per seconds over a mile long copper wire

Yes, but you need the bare copper wire without signaling. We operated a local ISP in the 90's and did exactly that by ordering so-called "alarm circuits" from the telco (with no dial tone) and placed a copper T1 CSU on each end. We marketed it as "metro T1" and undercut traditional T1 pricing by a huge margin with great success to the surrounding downtown area.

[phire]

Yes, the actual bandwidth of the last-mile analog line was much, much higher. Hence why we eventually got 8mbit ADSL or 24mbit ADSL 2.0+ running across it. Or even 50-300mbit with VDSL in really ideal conditions.

Though the actual available bandwidth was very dependent on distance. People would lease dedicated pairs for high bandwidth across town (or according to a random guy I talked to at a cafe: just pirate an unused pair that happened to run between their two buildings). But once we start talking between towns, the 32kbit you could get from the digital trunk lines was almost always higher than what you could get on a raw analog line over the same distance.

[immibis]

It's ISP←A→Telco←D→Telco←A→You

Traditionally both the ISP and you pay for analog phone lines from the telco. The telco uses digital internally (remember you and your ISP probably aren't at the same exchange), which puts a hard limit on data rate - there is no trick you can do to get more bits through than the bits used in the digital part of the call.

If you (as the ISP) buy enough lines you can get them delivered in digital format. A T1 is designed to carry 24 simultaneous phone calls, acting virtually as a bundle of 24 analog phone cables. So the obvious next stage was to have a modem that can handle 24 simultaneous connections on one cable.

Now you have ISP\_modem←Ax24→ISP\_muxer←Dx24→Telco←→Telco←A→User

The ISP's modem generates analog signals for up to 24 simultaneous incoming calls, and they pass into a multiplexer that connects 24 analog lines to a T1 line and they go through the telco digitally to users. The maximum bandwidth is still as before - the modem has to generate an analog signal that will still be receivable at the other end after A2D and D2A conversion. Even though the digital bandwidth for the digital part is 56kbps, the maximum achievable bandwidth through this digital-bottlenecked analog call was found to be 33.6kbps.

But the industry had an idea: by convincing the telco to install the modems into the user's exchange, the analog portion would only be between the telco and the user, without a digital segment in the middle of it, and therefore wouldn't be bottlenecked the same way. The same digital backhaul from the ISP through the telco was used, but instead of transmitting a digitised analog modem signal and therefore causing degradation of quality, it transmitted your actual internet traffic bits, up to 56kbps. The analog signal was made at the user's side of the telco and didn't have to fit within 56kbps when digitised.

Pedantically, the digital circuits are 64kbps but one bit in some bytes is used for call status signaling, which is okay for voice, but the ISP equipment can't predict which bytes have a bit overwritten (and it could be multiple if there are several hops) so it just used 7 bits in each byte.

[db48x]

No, it’s more like HomeModem ←A→ Exchange1 ←D→ Exchange2 ←A→ ISPModem. The digital parts were all inside the telco’s networks that connect the exchanges to each other.

> Couldn't you send data at megabits per seconds over a mile long copper wire without using modems at all (using just UARTs?).

No. The exchange is sampling the analog signal coming in over your phone line at 8kHz and 8 bits per sample. They just designed modems that sent digital data over that analog link, in a way that would line up exactly with the way the exchange will sample it.

[senshan]

The S/CNN for both trunk and nonloaded subscriber loop circuits shall not be less than 31 dB.

4kHz/2*log2(1+10^(31dB/10)) ~ 60.3kBps

[0] https://www.ecfr.gov/current/title-7/subtitle-B/chapter-XVII...

[kinkyusa]

Thank you!