What is Channel Capacity?

Any website owner understands the value of the capacity of a communication system. Really anyone understands this; how would you feel if you could only send a maximum of one word per email? The entire communication system would become much harder and less worth your time. Email (and the internet in general) has become so huge because people can send so much information so quickly; let’s see what factors are at play when it comes to trying to communicate a lot, in very little time.

One way to increase the capacity of a communication system is to increase the number of different signaling events. Imagine a string communication system in which plucking or not plucking the string to a certain metronomic pulse conveyed information. If instead of there only being pluck or no pluck options, there was additionally a hard and soft plucking possibility, and the difference between hard and soft plucks also conveyed information, then you have doubled the amount of information you can transmit at a given time.

thomas edisonThomas Edison had this same idea, which he then applied to the Morse code system. He was able to create 4 different current values which could be exchanged, allowing for way more information to be sent without changing lines.

Another issue: you can only add so many degrees of voltage difference into a Morse code language because of the limitations brought about by electrical noise; the narrower the difference between two signals, the more likely the difference will be totally unreadable due to random electrical noise and other unforeseen technical inconsistencies. In terms of trace amounts of unwanted electrical current, it’s a totally unavoidable factor; it’s caused by everything from heat to geomagnetic storms to the Big Bang.

Now we can step back and define the capacity of a communication system using two very simple ideas: how many symbol transfers for second (known as the symbol rate or Bod), and how many differences per symbol (think of it as the symbol space, how many symbols can you select from at any point?).

decision treeThese parameters can be thought of as a decision tree of possibilities; each symbol can be thought of as a decision where the number of branches relies on the number of possible decisions. Each path through the tree can represent a message, so the number of leaves on the tree can be seen as the size of the message space (the width of the base of one of the trees). The width represents how many messages one could be sent given the sequence of these event symbols.

Now we can begin to think of the capacity of a communication system like this: how many different things CAN you say given the decision tree of possibilities? If you have the string communication system and you can either pluck hard, soft, or not at all, you have only so many messages you can send given a time limit, and those messages will need more and more plucks to become refined. 3 minutes with that system would be very different than 3 minutes with a typewriter, for example.

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