When I originally went no contact with XABF, I left him a voicemail on his cell phone. He was still in inpatient rehab at the time, so they still had custody of his phone, so I knew he wouldn't answer when I called. I also called his therapist at the rehab, and left a message that I was going no contact.
At the time I felt certain I was through with the relationship, but I did not feel comfortable sharing that with him yet, so I left a message about how I wanted no contact with him so that I could work on myself, and that it might be a week, a month, or forever - that I would let him know if I was ready to talk to him again. (Of course he didn't respect these wishes, but that is a different story).
I finally communicated the breakup when he cornered me in my office, talking about how everything was all my fault but that he'd give me another chance if I came back now. I told him that I was done with the relationship, and that it was over forever. I would not have felt comfortable communicating this in person except that there were lots of people around (the conversation itself was private, in an area enclosed entirely by glass - nobody to overhear, but safe because everyone could see), and I had already mapped out a couple escape exits during his tirade in case he followed me after I said my few sentences. I let him shout on until I collected my thoughts, then I cut him off and escaped. (I mean escaped, because he did follow me, then hung around my desk for awhile waiting for me to return. I meanwhile had a vantage point on the second floor behind tinted windows watching his car in the parking lot.)
Sorry, I didn't mean to type all that.
But my point is, you don't have to communicate anything to him.
You also don't have to communicate anything to him right away.
You just have to do what you feel is right, when the time also feels right.