Asymptotic Error Free Partitioning Over Noisy Boolean Multiaccess Channels.

In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, and multi-access channel, where K active users (out of a total of N users) seek channel access. A solution to the partition problem places each of the N users in one of K groups (or blocks), such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative, case of K=2 active users and study the number of steps , where C_{1} and \xi _{1} are positive constants (independent of N ), and where \xi _{1} can be arbitrary small, the partition problem can be solved with error probability P_{e}^{\vphantom {R^{A}}(N)} \to 0 , for large N . Under the same scheme, we also bound T from the other direction, establishing that, for any , the error probability Pe^{(N)} \to 1 for large N ; again, C2 and \xi 2 are constants, and \xi 2 can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower bound in terms of T \geq (Cg +\xi )\log N for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing. [ABSTRACT FROM PUBLISHER]