Economic value increasingly takes the form of information, not of physical goods. Wealth therefore depends heavily on three things: our ability to store, compute, and communicate bits.
Of these three, by far the most limiting has come to be communication. There is no talk of a "memory crisis" or a "computation crisis": most of our computers use only a small portion of their available capabilities. Instead, we hear of a "spectrum crisis": the pressure on our ability to move information from one point to another. Cisco provides a summary of statistics. For instance, global mobile data traffic has more than doubled for the fourth year in a row.
Since 1949, our understanding of the limitations on our ability to move information has been governed by the Shannon law. Shannon's law tells us that "channel capacity", how much information we can move across a channel with Gaussian noise, is determined by two things: how much bandwidth we have available (the frequencies range we are allowed to use) and the signal-to-noise power ratio.
The elegance of Shannon's law is mixed with a certain sense of tragedy. Bandwidth and power are both limited physical resources. They can be expanded only at considerable expense.
However, the mathematics Shannon used in his proof did not consider the full set of possible signals. By using a technique known as "Fourier analysis", he implicitly limited himself to signals based on periodic functions: that is, signals that regularly return to the same set of values.
It is also possible to base signals on non-periodic functions, which are far more flexible. Generalizing Shannon's law to non-periodic functions leads to an important insight, which is that channel capacity is not fully determined by bandwidth and the signal-to-noise ratio. A third parameter appears, which has to do with "slew rate": the ability of a communication system to handle rapid changes in amplitude.
The importance of this fact is that slew rate can be improved by better engineering. One does not have to buy it at spectrum auctions, or pay for it with larger and more expensive batteries. There is a relatively straight-forward means to design our way around the spectrum crisis.
For those with an interest in the mathematics, it is available here.
Of these three, by far the most limiting has come to be communication. There is no talk of a "memory crisis" or a "computation crisis": most of our computers use only a small portion of their available capabilities. Instead, we hear of a "spectrum crisis": the pressure on our ability to move information from one point to another. Cisco provides a summary of statistics. For instance, global mobile data traffic has more than doubled for the fourth year in a row.
Since 1949, our understanding of the limitations on our ability to move information has been governed by the Shannon law. Shannon's law tells us that "channel capacity", how much information we can move across a channel with Gaussian noise, is determined by two things: how much bandwidth we have available (the frequencies range we are allowed to use) and the signal-to-noise power ratio.
The elegance of Shannon's law is mixed with a certain sense of tragedy. Bandwidth and power are both limited physical resources. They can be expanded only at considerable expense.
However, the mathematics Shannon used in his proof did not consider the full set of possible signals. By using a technique known as "Fourier analysis", he implicitly limited himself to signals based on periodic functions: that is, signals that regularly return to the same set of values.
It is also possible to base signals on non-periodic functions, which are far more flexible. Generalizing Shannon's law to non-periodic functions leads to an important insight, which is that channel capacity is not fully determined by bandwidth and the signal-to-noise ratio. A third parameter appears, which has to do with "slew rate": the ability of a communication system to handle rapid changes in amplitude.
The importance of this fact is that slew rate can be improved by better engineering. One does not have to buy it at spectrum auctions, or pay for it with larger and more expensive batteries. There is a relatively straight-forward means to design our way around the spectrum crisis.
For those with an interest in the mathematics, it is available here.
