Multiple access algorithms via group testing for heterogeneous population of users

The application of group testing techniques to the design of efficient algorithms for multiaccess systems with a heterogeneous population of users is studied. For a reservation system with binary (something/nothing) feedback, the authors present the procedure used to determine the optimal nested multiaccess algorithms. This procedure is not practical for moderate and large numbers of heterogeneous users because the computations and memory required for their determination are exponential in the number of users. Consequently, the authors introduce the notion of ordered algorithms and present the procedure for determining the optimal ordered algorithm. The computational complexity and memory requirements of this procedure are polynomial in the number of users. To show the effectiveness of ordered algorithms, the performance of optimal ordered algorithms for various orders is studied and compared to the performance of simpler suboptimal ordered algorithms and with optimal nested algorithms. The authors also study the performance of nested multiaccess algorithms (based on group testing procedures) for a direct transmission system with ternary feedback when the population of users is very large, and, for simplicity, a system with two classes of users