Coordination Through Shared Randomness

We study a distributed sampling problem where set of processors want to output (approximately) independent and identically samples from given joint distribution with the help common message coordinator. Each processor has access subset sources “shared” randomness. consider two cases - in “omniscient coordinator setting”, all these shared randomness, while “oblivious setting,” it none. In addition, may privately randomize. omniscient setting, when subsets at are disjoint (individually randomness model), we characterize rate communication required over multicast link. For two-processor case, optimal matches special case relaxed Wyner's information proposed by Gastpar Sula (2019), thereby providing an operational meaning latter. also give upper bound on for “randomness-on-the-forehead” model each observes but one source present achievable strategy general have arbitrary Also, more observe components correlated (with observing components), wish same random sequence. oblivious completely trade-off region between rates