Information of partitions with applications to random access communications

The minimum amount of information and the asymptotic minimum amount of entropy of a random partition which separates the points of a Poisson point process are found. Related information theoretic bounds are applied to yield an upper bound to the throughput of a random access broadcast channel. It is shown that more information is needed to separate points by partitions consisting of intervals than by general partitions. This suggests that single-interval conflict resolution algorithms may not achieve maximum efficiency.