# Theoretical limit of serial communication

1. Mar 3, 2013

### flatmaster

As I play on my new MacBook Pro and stream millions of bits per second through a cable, I find myself wondering about the theoretical limit of serial communication. I have noted that serial communication has become preferred over parallel communication over the years.

In fact, it's gotten so fast that the "bit period is shorter than the flight time "

http://en.wikipedia.org/wiki/Signal_integrity
see chip-to-chip signal integrity

So what's the "following distance" of our bits? How far down the wire does one bit travel before the next bit follows?

I approximate v = (2/3) X c
Assume 1 Gb/s

(2E8 m/s) X 1E9 bits/s = 0.2 m = 20 cm.

So each bit is about 20 centimeters "behind" the previous bit. Not sure what that means, but it's pretty cool either way.

What is the theoretical speed limit of such communication? The wikipedia article speaks of practical concerns of echoes and other things, but does not address a theoretical limit. Does physics put an upper bound on the rate this type of information transfer?

2. Mar 3, 2013

### marcusl

I don't understand what your post is about. Bit periods have been shorter than the flight time since the beginning of electrical communication. Even telegraph dots could be shorter than the time of flight when sent across the intercontinental telegraph lines in the 1800's.

As for a theoretical limit, Shannon's channel theorem expresses an absolute theoretical limit on the rate of data that can be transferred across a noisy channel.

Last edited: Mar 3, 2013
3. Apr 18, 2013

### MATLABdude

You might be interested in transmission line theory:
http://en.wikipedia.org/wiki/Transmission_line#Applicability

For the most part (certainly, for most of the work I do as a non-RF electronics engineer), the signal frequency is low enough and the distance it has to travel is short enough that transmission line effects don't come into play. To quote from the Wikipedia article I linked to, "[T]he length of the wires connecting the components can for the most part be ignored."

The rule of thumb is that once the length of the conductors exceeds about 10% of the wavelength of the signal (~2/3*speed of light / frequency), you have to account for the transmission line effects and properly terminate your conductors, or risk all manner of electrical nastiness (radiating away the signal power, signal reflections, etc.)

4. Aug 4, 2013

### meBigGuy

From wikipedia: In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.

So, the maximum capacity of a channel has a theoretical limit. To achieve the maximum rates multilevel/multiphase coding techniques are required (increased bits/Hz). Put another way, 2 level digital switching is like the telegraph compared to a radio. Think of the total information bandwidth of your cable TV connection.
The reason serial communication is preferred is that the connectors and cables are cheaper and more reliable and (the key point) IC's contain very cheap interfaces that can support these rates. As we move forward more sophisticated coding techniques will utilize the transmission bandwidth more efficiently. Designers will always jam as much as they can down a cable or optical fibre as cheaply as they can. (With modern IC technology, the IC pads required to support multi-conductor interfaces take up more area than the complex circuitry needed to deal with more sophisticated physical protocols, and most IC's are pad limited to boot)