Hi jbdog,DS4s do not come with DAB as standard, only option.
Citroen are peddling the built in DAB convertor at the moment, but at around £200 fitted you really need to like DAB over FM.
I have DAB built in on a Ford Galaxy and live in Lincolnshire, and have to say signals sh*t! The DAB signal is poor and drops out all over. Other disadvantage is that it 'pre-tunes' stations it can receive so you can only get what it wants you too. If I travel further south then it works fine, but not with me - so because of price I would check you have a good signal before commiting. As DAB not due to take over from FM for a while now (swap-over pencilled in for 2015 has been delayed/postponed as take-up not the same as digital TV).
As for compressor - yes a mini compressor is under carpet in boot along with sealing fluid for tyre, unless you paid for a spare wheel (posh!).