Address assignment for multiple-access systems based upon the theory of congruence equations

The authors discuss the address assignment via frequency hop patterns for a multiple-access spread-spectrum communication system. In such a system the receiver simultaneously communicates with a large number of transmitters (users), distinguished by their assigned addresses. In order to insure that the receiver correctly recognizes which users are active at the moment, it is necessary for the assigned addresses to possess minimum mutual interference. The authors define an algebraic construction for frequency hop patterns based upon the theory of congruence equations. The frequency hop patterns are constructed in such a way that they carry the address assignment and the message at the same time. The decoding scheme for the system is presented, and it is demonstrated that in both synchronous and nonsynchronous cases the mutual interference between the transmitted frequency hop patterns is minimal.