Can I represent the value by using this unit
I've never seen that notation but it's not good SI practice. 

Leaving out the 'i' for the moment, the 'd' in dB is the deci (x 0.1) SI prefix. Your 3.1 &times; 10-4 dB is 3.1 &times; 10-5 B (bel) so I would think that the correct way would be 31 &mu;B.

I can't find anything to back this up!