# Maximum Information Rate

I am reading B. P Lathi, Modern Analog and Digital Communication. In it, there is a topic where the author says that maximum information rate is two pieces of information per second per hertz.

Now I am a little confused as according to the sampling theorem, we need a minimum frequency of 2B samples per second.

Why does then the author say that only a maximum of 2*(maximum frequency) independent pieces of information per second can be transmitted, error free, over a noiseless channel of bandwidth Bhz.

• The are just assuming a binary signal. Mar 29 '18 at 17:05

Take a sinusoid of frequency B. Within a single cycle, the signal will hit its maximum and minimum amplitudes once each. Said another way, if the signal ranges from 0 to 1, then we'll measure the values of 0 and 1 once each during a single cycle.

Those maximums and minimums represent the pieces of information that Lathi is referring to.

Since we get one maximum and and one minimum per cycle, we have two pieces of information per cycle. And the maximum information rate is then 2 * B.

Sampling doesn't come into play here as we're using simple detectors to determine if maximum or minimum were reached.

But why did you consider a sinusoidal signal only. The signal could as well be a non periodic one, right?

I picked a sinusoid because it's easier to visualize and draw observations. A non-periodic signal yields the same results, but isn't as clear to observe.

With an analog signal, we use the maximum and minimum amplitudes of the signal because we can't determine if intermediate values are intended as valid signal points or if they are incidental values while in the process of traveling to a different value.

For example, if we have a sinusoid with an amplitude of +/- 1, then we'll cross the zero point twice. The receiver has now way of knowing if those zero values were meaningful or just incidental.

It's probably worth reviewing the Nyquist Rate, which is the source of this information rate. Nyquist was working in an analog world and trying to figure out how much information could be packed into a telegraph signal.

From there, look into the Shannon-Hartley theorem, which builds upon the work that Nyquist did and lends a more nuanced perspective of channel capacity.

• But why did you consider a sinusoidal signal only. The signal could as well be a non periodic one, right? B.P lathi in his book writes that a maximum of 2B independent pieces if information per second can be transmitted, error free, over a noiseless channel of bandwidth Bhz. The result follows from the sampling theorm. Mar 29 '18 at 12:24