Comment by mlyle

> An analog channel with the bandwidth and SNR characteristics of a landline phone line has (IIRC) a Shannon capacity of 30-something kbit/s,

The problem is that the ADC in the telephone exchange is not clocked coherently to your modem. You're paying various companding, quantization (time and level), etc, losses-- it is not a nice linear channel.

An end-to-end analog connection could be capable of significantly more-- while there's noise, there's no "8KHz cliff." A 45dB SNR for 0-4KHz has a >60kbps Shannon bandwidth, and there's not exactly a 4KHz cliff even with loading coils present.