Optimality of the recursive data exchange protocol

Multiple parties observe correlated data generated independently and identically (in time) from a known joint distribution. Parties communicate with each other interactively to enable each party to recover the data observed by all the other parties and attain omniscience. We characterize the asymptotic growth of the number of bits of interactive communication required by the parties to attain omniscience up to the second-order term. For the converse, we provide a single-shot lower bound for the required number of bits of communication, which yields the asymptotic result as a special case. It is shown that the knowledge of the distribution can be used to modify the recently proposed recursive data exchange protocol to render it optimal up to the second-order term. As a corollary, we provide a precise characterization of the reduction in communication for omniscience due to interaction.