What is the maximum transmission distance of the radio signal in the outer space which could still be understood? I’ll put this question in a form of a physics problem:
Transmitter at a point A sends a signal to a receiver at a point B. What is the longest distance in light years from points A to B for which receiver can still understand the signal?

Given:


Signal type: electromagnetic wave.
Signal frequency: frequency for which signal fades the least - probably radio.
Signal form:

Variant 1: beam of highest concentration possible.
Variant 2: full sphere.

Transmitter power: power of the most powerful transmitter known to be built in the Earth.
Receiver: sensitivity of the most sensitive receiver known to be built in the Earth.
Transmission medium: interstellar space.
Understanding of a signal:

Variant A: Can detect that the signal is not a noise.
Variant B: Can decode the information in the signal.
It cannot be said correctly, since we humans have hardly traveled to the moon and sent space probes to explore other planets in our solar system. So, theoretically anything might be possible. I'm trying to be a bit practical here. The only man made object that has gone really far is Voyager 1, which is at a distance of 18.7 billion kilometers (125.3 AU) from the sun. Although launched in 1977, it is the only live transmitter and receiver which is that far.

The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System. The communication system includes a 3*.7 meters (12 ft) diameter parabolic dish high-gain antenna* to send and receive radio waves via the three Deep Space Network stations on the Earth. Voyager 1 normally transmits data to Earth over Deep Space Network Channel 18, using a frequency of either 2296.481481 MHz or 8420.432097 MHz, while signals from Earth to Voyager are broadcast at 2114.676697 MHz.
As of 2013, signals from Voyager 1 take over 17 hours to reach Earth.

I agree that there are powerful transmitters in the world than what is present in the Voyager 1, but, most of them still remain untested. So, we can be exact with the measurements.