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The first inexpensive modem I ever purchased was a 300 baud direct-connect unit for the C64 User Port in late 1983. I recall that a couple of years later (1986), 1200 baud modems were affordable and I was able to make this significant (4X speed) upgrade. Then, by 1989, 2400 baud modems became affordable and I upgraded from a C64 to an Amiga with 2400 baud Supra Modem. The above timeline of about 6 years saw an 8X speed increase in what I would call affordable, consumer, "low-speed" modems. What came during the next 6 years felt quite different to me as I remember it.

The 9600 bps modems were out of reach price-wise as the early 1990s began. I remember the US Robotics Courier 9600 model being a large "beast" of an external box that cost nearly $1,000. What happened in the next few years seemed tremendous to me as, first, the price of these new "high-speed" modems fell to under $200 and, second, the speeds seemed to increase dramatically almost every year. By about 1996, 56 Kbps modems were inexpensive accessories that were often present in PCs. Naturally, this was a key to the growth in residential Internet access that followed.

The comparatively fast leap from 2400 bps to 56 Kbps was a 24X speed increase in roughly the same time it had taken for the 8X speed increase I experienced in the 1980s.

My question is what technology factors allowed for the rapid speed increases of inexpensive, consumer modems during this new generation of "high speed" modems that began with the 9600 bps variants and culminated with the 56 Kbps variants in only about 6 years.

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    "The comparatively fast leap from 2400 bps to 56 Kbps was a 24X speed increase" ... it's worth noting that it wasn't actually as large an increase as it seems on paper, because your 2400bps was symmetric, while 56K modems were asymmetric (usually only having 28.8Kbps upstream and 56Kbps downstream, IIRC). – Jules Nov 22 '17 at 16:53
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    Tangentially related: I love this picture of a 56k handshake. In particular, I love when they decide to turn off the echo suppressors. I always got the feeling of the modems looking at the PSTN and saying "quiet, dear, grownups are talking." – Cort Ammon - Reinstate Monica Nov 23 '17 at 16:02
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    @fluffy: Somewhat simplified, achieving a full 56K would require that modems be able to send an arbitrary voltage down the line on every sample, regardless of what was sent down on the previous one. The FCC regulates both the maximum and minimum voltages that may be sent, as well as the maximum difference between consecutive samples. Information must thus be coded in a way that guarantees that the maximum difference between consecutive samples will be within FCC limits. – supercat Nov 23 '17 at 17:58
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    @Jules 33.6k with V.90, 48k with V.92. Given good conditions, of course. – hobbs Nov 23 '17 at 22:38
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    This isn't helpful, but anecdotally -having a US Robotics Courrier HST in 1990 was outright magical. – Geo... Nov 24 '17 at 1:12
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Up to 9,600 baud it's just iterative application of fairly straightforward analogue-domain ideas as and when standards emerge. Then there's a significant improvement on the digital side that bumps to 14,400 baud. Incremental phone line improvements lead from there to 33,600 baud. Finally, a digital back end for the phone network provides 56k as a downward special case.


300 baud modems use simple frequency-keyed shifting: during the relevant 1/300th of a second the calling modem produces a 1070Hz tone for a 0, and a 1,270Hz tone for a 1. The receiving modem produces a 2,025Hz tone for a 0 and a 2,225Hz tone for a 1.

The change that brought 1,200 baud was a switch to phase-shift keying. Different symbols are now indicated by changes in wave phase, not frequency, and the number of symbols was increased from two (i.e. 0 or 1) to four or eight as the phone line permitted. Same frequency range but up to four times as much information per symbol = four times the bandwidth.

Different frequencies were used at each end of communications because phone lines are not two distinct and isolated channels, but rather each direction contains a slight echo of the other. The jump to 9,600 baud came through active echo cancellation — each modem measures the amount and delay of echo at the start of the call and subsequently keeps enough of a history to eliminate its returning output — and a switch to quadrature amplitude modulation, which is amplitude modulation of two sine waves, added together (and possibly slightly more famous for also being how colour is transmitted in the NTSC and PAL standards). That gives twice as many channels in operation, but with the active noise cancellation you're also no longer having to divide up frequencies between caller and receiver. So that's another multiply by four, to 9,600 baud.

The next leap is accepting a lossy signal through the Viterbi algorithm, via trellis modulation: it's a way to determine the most likely unobserved original signal that gave rise to an observed signal. So you're in the general realm of the Hidden Markov model. The mathematics predates modems and its application to modems was first published in 1976 but the paper that really made a splash with detailed empirical results is from 1982 and the corresponding ITU standard was agreed in 1990.

After that, phone lines get better so they up the underlying frequencies and tweak the tables underlying the trellis to get to 33.6 kbaud.

Eventually the phone network back-end went digital and 56 kbaud transmissions exploit exact phase alignment with the digital PCM samples — they're fed to the phone network directly as digital streams — and the fact that the final analogue hop isn't very far, so you can exploit a greater frequency range. Upload speeds remained at the old rate since the end-user has to feed analogue out and you'd be Nyquist limited even if you had an entirely lossless connection to whatever is digitising you given that its phase is unknown.

Outside of the standards process, there was also the Telebit Trailblazer, which went the other way: instead of trying to pack in complex symbols fast, keep them simple and slow but fill the entire potential frequency range with channels and dynamically enable or disable them based on which are getting through. That was an early leader but always proprietary.

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    @BrianH sorry, yeah, that's a little opaque. What I really meant was that a paper describing trellis modulation was first published in conference proceedings by Ungerboeck in 1976, owing its genesis to the Viterbi publication of 1967, but didn't manage to garner any significant attention until Ungerboeck published a second paper with extended experimental results in 1982. I'll correct my vagueness. – Tommy Nov 22 '17 at 21:07
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    The phone "backend" went digital in most places long before 56k modems came around. The transition from analogue to digital started way back in the 60's. In particular the G.711 codec standard was released in 1972, and its 64 kbits/s data rate forms the absolute speed limit of modems. (In practice the limit is 56k because of phone networks repurposing samples for signalling purposes.) – Ross Ridge Nov 22 '17 at 23:52
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    Great comment. One terminological niggle: "baud" isn't the right term most of the time. With 110 and 300 bps modems, "baud" is accurate because only one symbol per second was sent, but with 1200 bps and higher speeds, baud and bps differed as more than one symbol was sent at a time. If I recall correctly, 1200 and 2400 bps modems are 600 baud but transmit 2 and 4 symbols simultaneously, respectively, giving their net bps throughput. – Jim MacKenzie Nov 23 '17 at 22:49
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    The Viterbi algorithm is basically magic. It's the same algorithm that allows speech recognition to work, and is also pretty handy for any other tasks where you don't know exactly what parts of a message you've received (you have good candidates for each bit, but don't know which candidate is correct for each of them), but you can estimate how likely a particular message is. – Jules Nov 24 '17 at 10:54
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    @Mazura - the limiting factor was the long range connections between local exchanges, not the so-called "last mile". Note that the same wire that used to carry modem signals can now handle multi megabit DSL signals without interrupting your ability to use it for voice calls without an upgrade... – Jules Nov 24 '17 at 10:56
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I would say the big breakthrough is when V.90 was introduced. ISPs no longer had traditional modems installed to receive calls as the analog phone lines were replaced with 64kbit digital lines or multiplexed over T1 and similar.

This removed the digital to analog conversion that was done on the ISP side, allowing up to 56kbps from the ISP to the customer.

When V.92 came along it boosted the customer to ISP upper limit rate to 48kbps.

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    v.32bis and v.34 modems were the real paradigm shift for me. The Rockwell chipsets that supported these modes were inexpensive, and they were a massive speed increase from 2400 bps, which was the previous reasonably-priced speeds. (Rockwell skipped v.32, the 9600 bps speed, and went right to 14.4kbps v.32bis.) v.34 doubled the speeds to 28.8kbps (later 33.6kbps) and was a significant change, but the main benefit had already been achieved. – Jim MacKenzie Nov 23 '17 at 22:51
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I think the primary driver was the new availability of the Internet in the home. At that time modems were the primary method of getting online so it was worthwhile for companies to pursue ways to make modems faster. They implemented compression and better ways to encode the data so more bits could be transferred per second. They also focused more on increasing the download rate instead of increasing the upload rate, which allowed higher download rates be achieved. Finally, they hit a download rate of 56Kbps and and upload rate of 33.6Kbps. Then DSL came along...

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    This answer has cause and effect backwards. It is (incorrect) speculation. – dotancohen Nov 23 '17 at 8:59
  • v.32bis (14.4kbps) and v.34 (28.8 and 33.6kbps) modems pre-dated dial-up Internet in most areas, if not all. v.90 (the initial 56k) and v.92 (improved 56k) were definitely influenced by the demand for dial-up (although the latter arrived late enough that not all ISPs ended up supporting it, since broadband was starting to take off). – Jim MacKenzie Nov 23 '17 at 22:53
  • 14.4kbps modems certainly predated widespread Internet adoption among the general public. 28.8k modems may have been right around the time that widespread Internet adoption was beginning to happen. Wikipedia appears to put V.34 in Q3 1994 which coincides pretty well with the Internet boom around 1995-1996-ish. – a CVn Nov 24 '17 at 9:08
  • @JimMacKenzie - 14.4K, maybe. But commercial Internet connectivity was available and starting to become popular long before 28.8K modems were generally available. AOL's connection to the Internet in September 1993 was a major threshold, for example, or the launch of Demon Internet in the UK in 1992. – Jules Nov 24 '17 at 11:08
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    Wow an answer that actually answers the question. +1 – mathreadler Nov 26 '17 at 15:11
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The answer might be too simple and not as desired: Nothing revolutionary or new in particular.

The underlaying physics/mathematics and the technology neccessary was know since quite some time. Speed up was mainly driven thru general availability of faster chips and classic market forces: Fast enough DSP and lowered prices within an emerging mass market.

Eventually another great example that next to all development during the computer revolution wasn't driven thru revolutionary technology, but enabeled by improved manufacturing.

  • Softmodems were a kind of revolution given their affordability, but the main factor was the target market. – Gabriel Diego Nov 24 '17 at 20:16
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Porn

While the technology was always the same (actually, it evolved incrementally over this time), the network market changed quickly in the early 90s. Until the early 90s, household modems were used mainly to connect to text services, like BBS. That's until internet became mainstream and HTML became the main format on which people viewed content. Since you could embed images in HTML pages (in GIF or JPEG formats, back then), eventually people found that those there was a market for this kind of content and images (later also videos) demanded a much bigger bandwidth than plain text, which drove people to get the fastest available modems to not have to wait the images load for so long (progressive JPEG, anyone remember?). That was way before Youtube, Netflix or Lolcats even existed. My networks professor at university said that by mid 1990s to early 2000s porn dominated the internet by traffic.

Seriously, the main driver was that as personal computers became powerful enough to decode multimedia content, at first being JPEG/GIF images and MP3 music people started to share this content online (whatever was the content). These files usually had a size at order of 100KB to 1MB, which would take 11 minutes to 2 hours to download over 9600 bps or a fifth of that over 56kbps, assuming that the connection does not fail during the download.

Another driver also was pirated games online, specially those abandonwares that would fit a floppy disc or two.

Softmodems also helped

As the processing capability increased, the modems could offload much of their tasks to the main processor, thus they did not have to include a integrated processor or memory. They simply sent a interrupt to the microprocessor nearly every byte that they received, which greatly simplified the hardware design and reduced manufacturing costs. If you take a look on the design of these old US Robotics high end modem you will see that they included several components while the typical mid-late 90s modems had once single SoC.

  • Welcome to Retrocomputing. Do you have any citations for this (e.g. data to back up "My networks professor at university said that by mid 1990s to early 2000s porn dominated the internet by traffic")? If so, it would be useful to add them. – wizzwizz4 Nov 24 '17 at 20:00
  • psychologytoday.com/blog/all-about-sex/201611/… it is claimed that in 1999 40 of web searched were of porn. One could assume that porn content would be more data intensive than other kinds of data. I do remember also reading about the subject back in the day in a printed magazine, but I can't remember which or when. You could search online about web traffic share, I could not find much quickly. – Gabriel Diego Nov 24 '17 at 20:05
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    AFAIK, a softmodem is basically a sound card hooked up to the phone line. I'm not sure about your "interrupt every byte" claim; I thought they had buffers like regular sound cards do. (Small-ish for low latency, though.) The actual DSP work (and Hayes command-set processing) was done on the CPU. PCI made it possible for cheap cards to easily DMA to/from main memory, and fast enough to do in the background without using up all the CPU time. (Which that would be a problem if they really did interrupt every byte / sample). – Peter Cordes Nov 25 '17 at 3:10
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    The internet is really really great. I've got a fast comnection so I dont hace to wait. – Harper - Reinstate Monica Nov 25 '17 at 15:02
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    According to "a friend", porn on the internet predated HTML and the WWW, using FTP, Gopher and Usenet. – TripeHound Jan 25 '18 at 16:18
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The early 300 bps modems used frequency shift keying (FSK), whereby sound is generated at one frequency to represent a '0' and a different frequency to represent a '1'. Standards prescribed what frequencies to use, with one pair being used in one direction and another pair in the other. The relevant standards for 300bps are Bell 103 (America) and V.21 (elsewhere). Despite their common use at 300bps, these modems could be operated at any speed up to the maximum (and, in fact, usually a fair bit above that - I think some worked up to 450 bps). When you changed the input, the frequency being generated changed immediately, so the modem itself has no fixed baud rate. The signal processing for these was quite simple and could be implemented in analogue circuitry, but they were made cheap by having the circuitry made into integrated circuits (ICs) such as the AM7910 from AMD in the '80s. That chip implemented a good range of FSK standards up to V.23, which was 1200 bps in one direction and 75 bps in the other.

The next advance was by changing the encoding. Instead of using different frequencies for 0 and 1, a single frequency was used with the data encoded as a phase change. The first of these was V.22 which was a 600 baud (i.e. it sent 600 symbols per second) modem and could encode either one or two bits per symbol giving 600 bps or 1200 bps. This was better than V.23 because it gave the same speed in both directions (still by using a different frequency for each direction). It was possible to obtain specialist chips that implemented this. Because this type of modem (as with all faster ones) used a fixed baud rate, it did not allow encoding of data at any speed up to the top speed - you had to use the configured speed exactly.

At about this point, digital signal processing became cheap and simple enough to implement the processing required, so further standards generally were implemented that way, which also allowed more complicated encodings. The next advance was using both a phase and amplitude change to encode data. V.22bis used this to provide 2400 bps data over 600 baud (i.e. 4 bits at a time were encoded giving 4 * 600 bps).

All modems up to this point used a separate carrier frequency for each direction. This split the carrying capability of a phone line in half. The next advance was to use the same frequency in both directions, with suitable signal processing to subtract out the echo of the transmitted signal in order to get an accurate received signal.

The V.32 standard used the same carrier in both directions, and increased the signalling to 2400 baud, giving up to 9600 bps. It also added an alternative way to encode the 9600 bps. Like earlier standards, it allowed four bits of data to determine one of 16 phase/amplitude combinations for the carrier, but it also allowed it to determine one of 32 combinations (only 16 of which were possible for any given symbol) which traded more processing for greater resistance to errors.

Development proceeded to produce V.34, which was a fairly obvious continuation of the same techniques, using a slightly higher baud rate (3200) and more phase/amplitude possibilities to give up to 33600 bps.

However at this point development hit a limit. The phone network had once been analogue - basically just a pair or wires, which might have allowed ever faster data transfer using higher carrier frequencies or more finely divided symbol encodings, but analogue is expensive. Things change their characteristics through temperature, age, and other factors, so the network had been made digital. This meant that the signal was sampled 8000 times per second into one of 256 possible values, and this data was sent across the network to be reconstituted at the other side. This is a data rate of 64000 bps (56000 bps in America because one bit per symbol was stolen for signalling). However, it didn't allow a modem to use the full speed because even if you can generate exactly the 256 different levels, you cannot guarantee to synchronise the generation to the sampling, and the equipment (which was, of course, already installed in vast numbers of telephone exchanges) might not even be accurate enough to reliably sample all of the possible values. Consequently, V.34 is as fast as you can go.

However, there is a further trick that can be used. If we replace the modem at one end with something which handles the data directly in digital form, then the signal from the phone is still limited to about 32Kbps, but the data in the opposite direction can generate all 256 symbols reliably (128 in America). The modem can have a more sensitive detector and signal processing to analyse the incoming signal, allowing it to decode a signal which encoded up to 56000 bps.

The 56K modem was a strange anomaly - it only worked because one end of the call was purely digital. An obvious improvement would be to make both end digital - then they could use the underlying 64000 bps connection. Indeed, this was possible with ISDN - where Basic Rate gave you two such channels. However, phone companies made this excessively expensive, which meant that it was still considerably cheaper having an analogue phone line and a modem.

At that point modem development had hit a hard limit - further advances would require changes to the equipment at the telephone exchanges, which is where ADSL started - by making the last hop from exchange to customer encode data completely differently than data moving inside the phone network, it was possible to increase the speed much more.

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