Conditional and Relevant Common Information

Abstract Two variations on Wyner’s common information are proposed: conditional and relevant information. These shown to have operational meanings analogous those of in appropriately defined distributed problems compression, simulation channel synthesis. For information, an additional meaning is identified: a multiple-access with private messages, it the minimal common-message rate that enables communication at maximum sum-rate under weak coordination constraint inputs output. En route, weak-coordination problem over Gray-Wyner network solved no-excess-rate constraint.