Estimation of the Capacity of a Multi-User Vector Disjunctive Channel for Arbitrary Input Distributions

In this paper, we consider a vector disjunctive channel in which users transmit some binary vectors of length L. We estimate the capacity of this channel and derive a lower bound on this value. In addition, the lower bound is calculated both for the case of the Bernoulli distribution and for an arbitrary distribution for the case when users send 2 (L = 2) bits in one transmission slot. It is shown numerically that for $L$ = 2 and the order of the collision $t$ = 1, the Bernoulli distribution is optimal, i.e., it maximizes the capacity of the vector disjunctive channel.