The intention is to deliver voice messages to the stars. If you assume
a voice message carries information at a data rate of C bits per second,
doing the calculation of how far, D, the message can travel before it
cannot be received at that rate gives the following expression:
Cell phones code voice in the neighborhood of C = 10,000 bits/second. So let's take this as the minimum data rate that can support voice communications -- cell phones are extremely stingy with spectrum and try to pack voice signals into as little space as possible. So this figure is a reasonable lower bound.
According to the web site, Rt is approximately 2 meters and
&lambda is about 0.125 meters. Let's assume an Arecibo-sized
listening antenna on the other end (Rr = 150 meters)
that's chilled down to 3 degrees Kelvin. Plugging all that in gives:
One must remember that the above is a best case scenario.