A New Upper Bound On The Control Information Required In Multiple Access Communications

The minimum amount of information that should be supplied to transmitters to resolve traffic conflicts in a multiple access system is investigated in this paper. The arriving packets are modeled as the random points of a homogeneous Poisson point process distributed within a unit interval. The minimum information required is equal to the minimum entropy of a random partition that separates the points of the Poisson point process. Only a lower bound of this minimum is known in previous work. We provide an upper bound of this minimum entropy, and the gap with the existing lower bound is shown to be smaller than log(2) e bits. The upper bound asymptotically achieves the minimum entropy required to resolve per unit traffic. We then analyze the control information used to resolve the traffic conflicts in the splitting algorithm and in the slotted-ALOHA protocol, and identify their gaps with the theoretic bound.