The multiple access wiretap channel II with a noisy main channel

A two transmitter multiple access wiretap channel II (MAC-WT-II) with a discrete memoryless (DM) main channel is investigated. Two models for the wiretapper, who chooses a fixed-length subset of the channel uses and observes erasures outside this subset, are proposed. In the first model, in each position of the subset, the wiretapper noiselessly observes either the first or the second user's symbol, while in the second model, the wiretapper observes a noiseless superposition of the two symbols. Achievable strong secrecy rate regions for the two models are derived. The achievability is established by solving a dual secret key agreement problem in the source model. The secrecy of the keys in the dual source model is established by deriving a lemma which provides a doubly exponential convergence rate for the probability of the keys being uniform and independent from the wiretapper's observation. The results extend the recently examined WTC-II with a DM main channel to a multiple access setting.