Achievable partition information rate over noisy multi-access Boolean channel

In this paper, we formulate a novel problem to quantify the amount of information transferred to partition active users who transmit following a common codebook over noisy Boolean multi-access channels. The objective of transmission is to ultimately let each active user aware of its own group only, not others. To solve the problem, we propose a novel framework by considering the decoding as a process of removing hyperedges of a complete hypergraph. For a particular, but non-trivial, case with two active users, an achievable bound for the defined partition information rate is found by using strong typical set decoding, as well as a large deviation technique for an induced Markov chain.