Dial up modem vs. ISDN

1. From dial-up modem to ISDN, the occupied band in the frequency domain increases by 20 times (4kHz à 80 kHz), however, the bandwidth (bit rate) increases only from 56 kb/s to 128 kb/s. why the latter is not proportional to the former.

because ISDN has two digital data/voice channels and one control channel.
and the 128 kb/s is for -only one- ( correction *two* ) data/voice channel.
If you want more speed ask for ADSL on top of ISDN.

The I.430 protocol defines 48-bit packets comprising 16 bits from the B1 channel, 16 bits from B2 channel, 4 bits from the D channel, and 12 bits used for synchronization purposes. These packets are sent at a rate of 4 kHz, resulting in a brutto bit rate of 192 kbit/s and - giving the data rates listed above - a maximum possible throughput of 144kbit/s.

Basic Rate Interface (BRI, 2B+D, 2B1D) is an Integrated Services Digital Network (ISDN) configuration intended primarily for use in subscriber lines similar to those that have long been used for plain old telephone service. The BRI configuration provides 2 bearer channels (B channels) at 64 kbit/s each and 1 data channel (D channel) at 16 kbit/s. The B channels are used for voice or user data, and the D channel is used for any combination of data, control/signalling, and X.25 packet networking. The 2 B channels can be aggregated by channel bonding providing a total data rate of 128 kbit/s.

That doesn't seem to quite answer the question. I, my self, know nothing about these protocols, but it seems to me that there is some nuance in this topic that has yet to be revealed. For instance, is the old "dial up" protocol less reliable (i.e. is some of this "missing bandwidth" consumed by processes that shepherd the data more reliably resulting in a greater _actual_ relative data rate in some cases)? Are the two data rates disparate [dial-up rate vs ISDN rate], in that they are arrived at differently? Or is the bandwidth really the same, somehow, and something else is different?

The apparent poultry gain in data rate between the two protocols seems strange to me, too. The old dial-up-modems used audio tones to convey data over a phone line. That seems very inefficient to me, so inefficient that I would expect a much greater gain from a more mature technique (or is ADSL the _more mature_ technique?)

My memory of the time was that ISDN was developed when telephone services were a monopoly (think AT&T). No need to push the envelope when you are the only service provider.

High speeds modems for POTS use were driven by a convergence of a new need for speed (internet), dsp maturity, consumer demand, and industry driven (not AT&T) standards. I remember products being shipped before standards were finalized as companies attempted to grab market share, and a few incompatibilites due to that behavior. Overall, things progressed fairly quickly and smoothly.

Where did you come up with 80KHz bandwidth for ISDN by the way? ISDN was delivered over the same POTS infrastructure, I believe requiring 2 pairs (could be wrong here).

Dial up modem uses analog audio frequency signals for phone lines to transmit voice only. A low pass filter that has a passband of 3.2khz was used and therefore everything above 4khz was attenuated. It was assumed that only 7bits was reliable sending using dial up modem. If 7 bits are sent on each sample and there are 8000 samples each second that yields to 56 kbits/sec.A typical ISDN has 3 channels 2 bearer channels for voice and data, and a D channel for signaling a control. A bearer channel is a standard voice channel of 8 bits per sample and there are 8000 samples per second which comes out to 64kbits/sec for 1 channel and 128 kbits/sec for the two bearer channel.

test the dial up.. 16K plus 4 to 1 compression.. isdn is the slowest way to spend money, but night and day above dial up..

ISDN is from 1988, before the mainstream internet time.
And it was developed to work on long distance using the old cabling junction boxes etc.

Yes typical it is possible to work much faster, then it needs new equipment cabling etc. ( in case they are old)
Because soon after (A)DSL came on the market and several providers and yes the misty world that you pay for a high speed connection and most of the time only have half of the speed.

I have at home ISDN and ADSL, when there is a lighting storm the over head cables work as nice antennas and ADSL does not work or my modem just burns out incl. the filter and the lightening protection.
I use then my ISDN as backup yes way slow (128Kb ISDN and not 20Mb ADSL) I have already 9 years my isdn modem and after every burnout the telephone company replaces my ADSL modem ( +/- 5 to 6 months)