In article <3fc84276$1_2@news.tm.net.my>, cfs717@tm.net.my wrote:

If the Arecibo radio telescope could be transported to Alpha Centauri,
scaled up in size and then pointed back towards Earth, then a telescope
with a diameter of over 33,000 kilometers would be required to
detect UHF television pictures leaked from Earth. This is equivalent

The figure that you should be using is the 0.3 LY carrier detection range,
not the 2.5 AU full channel detection range, making the required diameter,
keeping all other assumptions the same, about 15 times that of Arecibo.
The 2.5 AU case does have some relevance to digital systems, with no
distinct carrier.

http://www.computing.edu.au/~bvk/astronomy/HET608/essay/

Whilst I'm quoted here, I didn't choose most of the assumptions.  My main
contribution was to revise the noise level and detection threshold
assumptions.

One particular assumption is that the time bandwidth product is one.
That's reasonable for the 0.1Hz carrier, as it means an observation
time of 10 seconds, which is consistent with drift scan searching on
a narrow beam, but, for the 6MHz full channel, it might be better to
to still use 10 seconds, in which case the detectable signal level
is reduced by sqrt (60,000,000) or 7,750 and the necessary receive
aperture diameter reduces by a factor of 88, although that is still
somewhat large, and an Arecibo type feed would need to be moved
rather fast to keep the source in beam.  (This increases the full
channel detection range for Arecibo to a little over a light
day.)

The project Phoenix people reckon that they will be able to detect TV
carriers from several stars using a fully populated 1 square km array.
In part that probably reflects an assumption of observing a single
source for a lot more than 10 seconds.

Once you have found a signal, analogue TV has a lot of redundancy, which
means that you can probably recover a workable picture when the signal
is below the noise level (if you look at a grainy distant transmitter,
the grain is the noise, but you can integrate the image from frame to
frame and, even if there is movement, you can use what you know about
the nature of the image and what preceded it, to make a good prediction
of what was actually transmitted).  You cannot get your 7,750 times
improvement from averaging over 10 seconds, but in reconstructing
the grainy picture, you are averaging the same point over many frames.
One probably only gets about a factor of 3 to 5 improvement in antenna
diameter over your figure from this factor (which can't be combined
with the 88 one above).

One other point.  The calculations assume a particular illumination
efficiency at the receiver.  That is a bit optimistic for an ordinary
low noise receive dish but may be very optimistic for Arecibo, as it
doesn't use a lot of the available surface in any given direction.
0.1 might be closer to the truth.  (This is something I learned
fairly recently, but, probably, ought to be fed back into the 
sci.astro FAQ).  As the other people involved with this section
of the FAQ are more likely to be found in sci.astro.seti, I'm
adding a cross-post to that group.