The famous example illustrating PD created by Albert W. Tucker does have no communication - so that parties don't coordinate and cooperate with each other - but in this case with thousands of parties, there was no way to coordinate them all, or communicate with them all in time, or trust them all, so it still counts. It's possible to set up prisoner's dilemmas with communication, say in cases where it's a one off and the parties have every reason not to trust each other's word.

Communication is meaningless in prisoner's dilemma.