Secrecy Rates for a Channel With Two Senders and Two Receivers.

Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El~Gamal and also the method of output statistics of random binning. An intriguing synergy is observed between the achievable rate expressions arising from the two techniques: the rate region of the latter is simplified via a constraint that is discovered while deriving the former rate region. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that characterizes the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels.