Z. Goldfeld, G. Kramer and H. H. Permuter
Accepted to the IEEE Transactions on Information Theory, August 2016
The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived. Without leakage constraints the inner bound recovers Marton’s region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios.