Ok I see a lot of stuff being tossed about here so I will do a quick and dirty FAQ on Cries of Alderaan storyline for those that need to finish it.
1) Do I have to collect Rebel discs if I am an Imp or Vice versa to complete the quest?
A) NO! You can collect either sets Reb or Imp, if you are Reb, Imp, or Neutral and turn them in to a faction recruiter. You WILL get the same faction increase, creds, and badge. It really is dependent on which side you turn the discs to get which faction. (Imp recruiter...900 Imp faction, Rebel Recruiter...900 Rebel faction)
2) Can I gain the discs over and over to gain the faction?
A)NO! You get a one time shot on the faction and badge. Otherwise all you get is another 600 creds.
3) Where do I get the discs?
A) From every humanoid NPC. Meaning pretty much everything on two legs. Thugs, hermits, Valarians, Jabba swoops, gungans, theives, rebel troopers, storm troopers, meatlumps, ragtags, and everyone else has a chance of having a disc. You best bet is to find a place where some low level NPC consistently spawn. Corescant City in Correllia has several places on the outskirts of the city that have places like this but a LOT of cities do as well.
Also, you can get them by getting treasure maps and digging them up. I found one in a treasure box.
4) I got a "encoded disc" but which one is it?
A)Click on the disc and let the radial menu come up. Look for the 'decode' button and it will decode it to identify what it is. ENCODED DISKS (without the name Imperial or Rebel) HAVE A CHANCE TO BECOME A REBEL OR IMP ENCODED DISK ONCE YOU DECODE IT.
5) How do I find out what number I have on my Rebel or Imp Disc?
A) Double click on it in inventory to bring up another window..the detail window. Look at the title..it will say something like "Rebel Encoded Transmission (2/4)" or something like that.
6) Ok so I got all four discs...now what?
A) Click on one disc and click 'read' in the radial. This will bring up what it is and a button that says "Assemble". Click this and your four will become one. You may now turn this in the recruiter of your choice.
7) How do I turn it in to the recruiter?
A) Drag the completed discs over the recruiter. He/She/It will take it and give you the reward.
8) Whats with the jumbled text that shows aftrer you turn it in?
A) That is the second part....You can get a chance to decode parts of it but it is tough. There is an ongoing forum thread already set up to try and decipher it here.