Hi, interesting to try a high value root crop. This seems to be the go to Google for hydroponic Ginger:

http://fshs.org/proceedings-o/2003-vol-116/051-52.pdf

It is not exactly clear to me, but it seems they simply made a huge growing tray inside the greenhouse and filled it with coarse perlite. They then mixed up something very close to the hydroponic special fertilizer many of us are using (5-11-26) including their magnesium source (for which we use epsom salt). Seperately they made a pH down (with sulfuric acid) and Calcium nitrate solution. They kept the perlite rather immersed and watched the the EC and pH, and kept adding it in to keep the roots happy. There was a small amount of rot after they finished but it sounds like they blamed themselves for not harvesting the ginger on time and leaving it immersed too long. They couldn't taste the difference in taste between the hydro and outdoor raised bed control they did, but had 50-100% higher yield per plant hydroponically with no pest problems.

Sounds like a fun experiment... here's a picture of a hydro-grown rootpile to get anyone's blood pumping and maybe even willing to try sushi!

http://smallfarms.ifas.ufl.edu/crops/vegetables/pdf/GingerRoots.pdf