Transmission of partitioning information over non-adaptive multi-access Boolean channel

In this paper, we propose a novel framework to study the transmission of partitioning information over a Boolean multi-access channel. The objective of transmission is not for message restoration purpose, but rather to make active users partitioned into distinct groups so that they can transmit their messages without collision subsequently. Random coding and MAP decoding are employed for achievability proof under a novel framework for strong coloring of a resulting hypergraph, which is created by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple but non-trivial case with K = 2 active users. The derived achievable bound is shown better than the converse bound of group testing, which is intended for identification of all active users, rather than the partition we are seeking, thereby further demonstrating the uniqueness of our problems.