Gee professor, how about using a very wide band transmitter receiver arrangement so one can transform data gathered over long intervals required by the packaging for space travel into short time signals containing all the information once it is collated at the transmitter. Benefits:eliminate noise problem of space distance, and deliver very large amounts of information is just a couple microseconds in redundant pulses. Problems: very large antennas on board craft which are already being used, and sure its sub threshold, but, the signal is known exactly so that shouldn't be a problem.
Just sayin'
Eliminate the noise problem by making it vastly worse?!?! What are you smoking?!
To receive the data the signal must be above the ambient noise level. The ways of accomplishing this are bigger antennas (narrower focus), more power and reducing the range of frequencies being used.
Big dishes take mass, big generators take mass. There's a limit to how far you can go with either of these with something you're sending into the sky on a tail of fire. That leaves only the last option--narrowing the frequency band.
The reason narrowing the frequencies helps is that the noise is across all frequencies. The wider the band you are looking at the more noise you receive.
(Note that in some special cases where you already know most of what it's going to say you can receive somewhat below the noise floor. The GPS system works this way--the only way you can find the signal is by looking for known patterns in the noise. If you don't know what to look for you can't find them at all with an ordinary small GPS receiver with it's omnidirectional antenna.)