Packet Switching in a Channel without Feedback

The authors consider transmission of packets from $M$ transmitters to one common receiver over a channel without feedback. Undesirable superpositions of packets (i.e., conflicts) may occur in the channel. It is assumed that the transmitters do not know the packet propagation time to the receiver. The problem of determining the system capacity region $\mathfrak R$ is considered. It is shown that region $\mathfrak R$ coincides with the ergodicity region of an ALOHA system with feedback. A switching matrix that yields any rates from $\mathfrak R$ is obtained. Generalizations of the problem are given. A similar system with equal rates for all transmitters was considered earlier by J. L. Massey [IEEE Int. Symp. on Inf. Theory (Les Arcs, 1982), IEEE, New York, 1982, p. 101].