Common Randomness Generation from Sources with Countable Alphabet

We study a two-source model for common randomness (CR) generation in which the sender Alice and the receiver Bob generate a common random variable with a high probability of agreement by observing independent and identically distributed (i.i.d.) samples of correlated sources on countably infinite alphabets. The two parties are additionally allowed to communicate over a noisy memoryless channel. In our work, we establish a single-letter lower and upper-bound on the CR capacity for the proposed model. This is a challenging scenario because some of the finite alphabet properties, namely of the entropy can not be extended to the countably infinite case. We use a generalized typicality criterion, called unified typicality, which can be applied to random variables on countably infinite alphabets.