Why is 56k the fastest dialup modem speed?

by Alex Freeman

If you've ever had dialup internet service, or still do, or just know someone that does, you have probably heard terms like "56k modem". "56k" has become almost synonymous with dialup Internet access. But it's such an arbitrary number. It's not divisible by ten, it's not a power of two... so why was it chosen as the fastest dialup speed? For the answer, we will have to travel back in time quite a while.

Our visitors from Google should be warned that this is not a "stripped down" explanation; it is intended for relatively technical readers. But if you really want to know where this magic number comes from, you need to understand some of the technical background. As we shall see, "56k" was not just pulled out of a hat.

Setting the baseline

First, let's be specific about what we mean. A "56k" (sometimes the 'k' is capitalized and sometimes not; the reasons are not really relevant here) dialup modem can download data at up to 56 kilobits per second. That is a theoretical maximum of the hardware; for various reasons (and yes, we'll get there) this speed can never actually be achieved. Upload speeds are considerably slower.

This was all codified in 1998 in the ITU V.90 recommendation, which merged two competing standards (X2 from 3COM and K56flex from Rockwell Semiconductor). V.92 came slightly later, and introduced various tweaks; mostly, it increased the maximum upload speed. Any modern dialup modem will conform to one of these standards.

Got all that?

Long, long ago

Bur story starts much earlier. Long ago, when the phone networks were still completely analog, when the first real phone networks were being built, the engineers that were designing them faced a decision. They needed to determine how much bandwidth their networks had to have in order to ensure adequate voice quality. Too little bandwidth, and users wouldn't be able to recognize the voice of the person on the other end. But the more bandwidth the system was specified for, the more difficult (and expensive) the network was to build.

Ultimately, they settled on approximately 3.2 kHz. The implementation for this is pretty simple: the phone lines in individual houses run to boxes owned by the phone company, which pass all voice traffic through a lowpass filter. This filter has a passband of 3.2 kHz, and a stopband starting at 4 kHz. The entire signal at 3.2 kHz and below is preserved, everything above 4 kHz is attenuated heavily, and as for the frequencies in between, well, we just don't worry about those. Problem solved.


Fast-forward to 1962. Ma Bell begins using T-1s to connect its switching centers. T-1s are a digital communications link, not analog. The entire phone network goes digital. In a modern phone network, the only analog communication is between an individual house's phone line and the phone company's box.

T-1s are a particular form of DS-1 (Digital Signal 1). They implement the DS-1 protocol, with an AMI line code (alternate mark inversion; a "0" is 0 volts, "1"s alternate between logic high and logic low), over twisted pair cable, for a distance of up to 6000 feet (very roughly 1 mile). Now that we've gotten all precise, I'm going to play a bit loose with terminology and call this "a DS-1" because it makes what follows easier to understand. And it's very nearly correct.

A DS-1 is made by multiplexing 24 DS-0 streams. Each DS-0 corresponds to a single phone line; that is, a typical house gets one DS-0. Why 24 of them in each DS-1? No idea. Most likely that was that was the maximum possible without overstressing the equipment that was available at the time. The most comparable European standard, E-1, multiplexes 32 channels together (1 is used for internal signaling purposes).

In order to get your voice data onto this digital network, it must first be digitized. So now instead of just going through a lowpass filter, it goes through a lowpass filter, then is sampled, and then is run into an analog-to-digital converter that assigns a numerical value to the amplitude of the signal at the instant it is sampled. Simple, right?

As we've said, the lowpass filter cuts off all frequencies above 4 kHz. This means that the filtered signal can be sampled at 8 kHz (which is to say, it is sampled 8000 times per second) with no fidelity loss. This is the Nyquist Rate; any signal sampled at a rate equal to twice its highest frequency component can be completely reconstructed. So now we have turned our analog signal into a discrete-time signal running along at 8000 samples/second.

Next we want to quantize our signal so that we have a purely digital signal. For this, an 8-bit analog-to-digital converter (ADC) is used. Here there is some fidelity loss, but not enough to be detectable to human ears. Fidelity could be improved by using, say, a 16-bit ADC. But that would cost more to manufacture (at the time, a lot more) , and would mean that all the other hardware has to be built to transmit twice as much data. So 8-bit it is.

For those of you keeping score at home, that means we now have a signal that transmits data 8000 times each second, and transmits 8 bits of data for each of those samples. 8 bits/sample * 8000 samples/second yields 64 kbit/s (64 kilobits per second). So why can't dialup modems go up to 64 kbit/s? The short answer would be "historical reasons".

We're with the band

The more complete answer is "control data". Most communications networks need to transmit two kinds of information. The first is data; for phone networks, this is voice data. The second is signaling information, the control data that lets the network communicate status information with itself. There are two ways to send control data: "in band" (where it is packed in with the data) and "out of band" (where it gets its own separate channel, possibly in an entirely different physical medium).

After we've created the 64 kbit/s data stream that fills up our DS-0, it needs to be multiplexed into a DS-1 for longer-distance transmission to the phone company's switching station. And the DS-1 has control data to carry. The Bell engineers decided to send that information in band.

But how do we go about packing this data in? One way is to "steal" some data bits and replace them with control data. And that is exactly what the Bell engineers did.

Petty theft

A DS-1 transmits data in frames. Each frame contains one complete sample from each DS-0, plus a framing bit. Since there are 24 DS-0s multiplexed to make each DS-1, and a single sample from a DS-0 is 8 bits of data. 24 * 8 makes 192 bits. Toss in the framing bit and you have 193 bits.

So we have our 193-bit frame, and we want to pack some control data into it. How? Every 6 frames, the least significant bit of each voice channel is "stolen". The data bit is thrown out, and control data is sent instead. Because it is the least significant bit that is lost, this very slight alteration to the voice signal is not detectable by human ears. Everybody's happy.

Enter the modem

That system worked fine until people wanted to transmit more than just voice on these networks. If you're sending voice, losing the least significant bit of every sixth byte is no big deal. If you are sending data, it is a very big deal. Neither modem has any way to know which bytes will be affected. Maybe this sample, maybe the next one. This is a problem.

The solution is simple enough: assume you are always going to lose that least significant bit. Assume that you can only reliably send or receive 7 bits with each sample. When the receiver gets its data, it simply throws away the least significant bit of every byte. That yields a maximum data rate of 7 bit/sample * 8000 samples/s, or 56 kbit/s.

And that is where the term "56k" comes from.

So why can't I actually connect at 56 kbit/s?

Anyone that has ever used a dialup modem knows full well that they don't actually get to connect at that speed, though. And that their connection speed varies each time they dial in. There are two factors at work here.

The first is the FCC. If you are in the United States, the FCC places a restriction on the power output of devices connected to the phone network. The result is that you will never be able to connect at a speed faster than 53.3 kbit/s.

The second is the overall complexity of the phone network. 56 kbit/s (or 53.3 kbit/s) requires very good operating conditions, as it is really operating beyond the paramaters of what the phone network is required to be capable of. Operating at these speeds requires that there only be one ADC between the user and their ISP (which is not guaranteed to be true, but typically is), and that the copper wiring in the user's "local loop" have very good electrical properties. Part of the dialup process that is used to initiate a connection is an evaluation of the overall quality of the connection; if it is determined to be lacking, the modem will automatically drop down to a lower data rate.

About the Author

Photo of the author

Alex Freeman is the creator of 10stripe.com, and has entirely too much free time.

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