Can we save thermal noise?

In communication as you know there is something called thermal noise which is totally random and can mess up your data. There are some encoding stuff for data in order to avoid this. What I wonder is why do we try to encode our data while the problem is caused by thermal noise.

Can we make a device that both sends data but at the same time sends a blank signal so that data we sent will be data + noise while the blank signal will be 0 + noise = noise. So that receiver can subtract this noise from the data we sent and get the correct data without any encoding stuff. Is it possible or thermal noise is so random that even the blank signal's noise and data's noise will be different?

• You seem to be describing a dual channel system - one for the signal and one without. Wouldn't both have separate drivers and receivers each generating their own thermal noise - and yes random means random! Commented May 23 at 14:21
• It's a differential signal (see RS-485, Ethernet, USB, HDMI). Not exactly, but similar idea. But it only works for common-mode noise. And not every noise is common-mode. Commented May 23 at 14:36

No: thermal noise is independent per channel, and the difference between two uncorrelated noise sources is Vrms(total) = sqrt(Vrms1^2 + Vrms2^2). This is true whether adding or subtracting them, actually, so the total noise only goes up.

If the noise correlates between channels, common-mode noise on a differential signal for example, it can be canceled out.

There is also limited means by which thermal noise can be opposed: the negative feedback of an amplifier can effectively reduce thermal noise of a resistor (under what conditions exactly, I'm afraid I forget); this isn't prohibited, because the amplifier consumes exponentially more power in doing so, than the thermal noise power generated/opposed, and in effect it's a refrigerator -- albeit a wildly inefficient one as electronic noise is a single degree of freedom so the absorbed power is truly microscopic. I don't think this can be applied generally, though.

Thermal noise (white-ish) presumably originates in the front end.

If you have two front ends the thermal noise will be uncorrelated so the thermal noise in the difference will be higher than the thermal noise of each one alone (ideally higher by about $$\\sqrt{2}\$$ or about 40%).

In special cases, this works. In a charge-coupled device, to measure the charge in a pixel, you first set the potential of the charge sense stage's gate by connecting it to a fixed potential through a switch. Then you disconnect it. The disconnection thermally contaminates the potential (kTC noise).

You can cancel this using correlated double sampling. First, measure the contaminated potential, then transfer a pixel's worth of charge to the sense stage, and measure it again. Subtract the measurements, eliminating the kTC noise (thermal noise from the sense amplifier itself remains). The charge transfer itself is uncontaminated: in a well-constructed CCD, the transfer moves every electron in the pixel.

But if no such pair of correlated channels exists (the usual case), the technique doesn't work.

This would work in theory if you could send the same noise on the second channel. The nature of thermal noise, where each resistor in the system makes it's own unique random pattern of noise, means it is not practical.

There are other noise types where it is practical though. For example, if your sending circuit is in a noisy location such that the circuit's ground has noise on it. Perhaps it's in a box with a buck converter, or it's just far away and uses a different ground point. We can take two wires from this circuit to our receiver, one attached to the circuit's output and one to its ground. We then make a differential measurement on those wires and get the signal without the noise. This also works for noise picked up by the wires - as long as they run together, they pick up the same noise and we can use a differential measurement to reject the noise. Noise which appears on both wires is known as "common mode" noise.

We can actually improve on the above. Instead of sending the signal and ground, both carrying the same noise, we can send signal on one wire and -1*signal on the other. This is referred to as a differential signal, or a balanced signal, and gets you a factor of 2 in signal-to-noise without increasing signal voltage.

Sending a blank will help you estimate the parameters (mean, variance, etc.) of the noise, but the noise itself is random and uncorrelated. If you are sending symbols slowly, you may be able to process out well-estimated noise. But at high speeds, you run into the limits of just not having enough samples per symbol to use such statistical approaches.

One use of your approach is that you can estimate the noisiness of the channel and tweak your algorithm to provide the best bandwidth for that particular level of noisiness.